Friday, September 1, 2017

How to Factor the Quadratic Equation to know Variable Quantity?

An algebraic equation is one of the common math problems which include linear, quadratic and other higher degree equations. Solving out these equations is difficult sometimes due to the tough coefficient. If your kid is facing any difficulties in solving the algebra homework, then you can help by knowing the easy method for its solution. You can access the digital platform in which you just have to enter the coefficient then you can achieve the variables.
Without the graphing calculator or algebraic calculator, it is difficult to solve but it is not so. You can use the formula method or use the factors to determine the variable values. How to factor is the most common question that would come to the mind of the learner.  

Quadratic Equation
Quadratic Equation

How to solve the quadratic equations?

Before solving the quadratic equation, you should understand its basics. To understand the quadratic equation, consider an example as- 2x² + 6x + 9 = 0 

A quadratic equation is written above in which x is the variable, and the number with X is coefficients and remaining one is constant. To get the math help by the calculator, you just have to fill the coefficient and constant values into the software. You can easily get the variable value which may be negative or positive. On the other hand, you can use other methods. These methods are as-

Solve by formula method 

A and B are the coefficients of   and x respectively, and C is the constant value available in the algebraic expression. Here in the equation, you have  
A= 2
B = 6
And c = 9

Now put the value into the equation, you will get,
After solving the numerical expressions, you can get two values. One is negative, and other one is positive.

By Factor method
Factor method is nothing but breaking out the expression into two parts i.e. taking out the common factor from the expression. Also, it is the simple and fast method to get the variable values. In this method, you don’t need to remember the complex formula. To better understand the factor method, you should know how to factor the expression. Consider an example to understand the factor method better and solve the quadratic algebraic equation.
2x² + 6x + 9 = 0

Follow the steps-
2x² + 2x + 3x + 9 = 0
In this step, the central part is divided into two parts
Now, you have to select the common factor out, i.e.
2x² + 2x + 3x + 3 = 0
2x(x + 3) + 3(x + 3) = 0

Take out the common factor again,

2x(x + 3) + 3(x + 3) = 0
(x + 3) (2x + 3) = 0
Now, you have two factors i.e. (x + 3) and (2x + 3)

Keep both the factors equal to zero to achieve individual values
X+3 = 0
X = -3
Again,
2X + 3 = 0
2X = -3
X = -3/2

We have two values of X which are determined by the factor method i.e. X = -3, -3/2

By this method, we do not have to face any complex calculations as faced in formula method. Here the most complex calculation is to choose the common factor. Also, you can find the simple method, but these methods are best to get the accurate answers. To check the answer, you can put the variable value into the expression. If the quadratic equations become zero, then you have right variable values.

Tuesday, July 18, 2017

Learn the most Basic Steps for Solving an Algebra Equation

Mathematics has been one of the most interesting subjects among the learners. There are numerous interesting topics that are available for the learners of mathematics. One of them is solving an algebra equation. There are many important concepts that need to be understood and many other methods that need to be learned in this respect. There can be many easy ways through which the beginners can become perfect in solving a linear equation. Understanding these would help the readers to get better at them. Therefore we are going to discuss some most common and interesting facts about the steps involved in solving linear equations.
Algebra Equation
Algebra Equation

Let’s understand better
Linear algebraic expressions can be said to be the equations with any common variable like “x”. However, these do not have anything complicated like x⁄y or x² . Therefore these are much easier to solve than any other equations you may have. There are no square roots or anything more; there are just simple variables and operations. So if you are looking out for such simple equations then relax for you will be able to complete your algebra homework on time.  Solving simple equations is just like the ‘fill in the block’ exercises in your early schooling years. However here you need to ascertain the exact value that will be working in place of the variable “x”.

You may get to learn more advanced methods in respect of solving these equations. The first and the most important this that you need to know in this respect is to separate the variable from the other part of the algebra equation. For this, you may also need to consider the rules of LHS and RHS. This way you will be able to bring in the answer i.e. the correct value of x. Let’s understand this with an example. For example, the problem is: 
Solve x+9 = -30
Now the main thing you need to ensure is to isolate x from the other contents in the equation. The next will be: x =  -30-9 ;
When you bring 9 to the other side in order to separate x from the equation, you need to focus on the sign change. You need to perform exactly the opposite operation in order to simplify the equation. Also, you need to consider the negative sign with 30. This is important as it will play a major role in getting the solution. The digit 9 which is added on the left side will now be subtracted when it moves to the right. So now the solution for x is simple.
x = -21

Thus it is very easy to solve linear equations. However, there are many other methods that you need to learn and can be applied to get the right answers for these equations. But this is the basic rule that you need to follow in respect of all types of equations. Therefore now you can easily try to complete your algebra homework. A bit of practice will always be the best to make you perfect for solving algebra equations without any help. Also, it will always improve your perfection.

Saturday, July 1, 2017

How to Solve Quadratic Equations within Seconds?

A quadratic equation is a polynomial equation which includes a variable with a high degree. In algebra, the equation includes some numbers and a variable. The value of a variable is lies between the quadrates. The number of values of the variable is completely dependent on the degree of it. If the equation includes a higher degree of two than there are 2 values are available of unknowns. To solve quadratic equations, you need to follow some rules, but it usually takes more time. In competitive exams, the time plays an important role to qualify it. We cannot spend a lot of time on single questions. That is why it is best to know the tricks to solve quadratic equations.
Before going to solve any example, first, understand the basics of it,

Consider some example like 
In the first equation, the higher degree of a variable is 2, and in the second one, the higher degree is 3. So we may get the value of x 2 and 3 respectively.

The standard form of quadratic equation is  ax²+bx+c=0
So, we can find out the value of x by the formula as, X =  

If we consider the second 2x³ +12x +8=0 then it can be solved by above equations

The values a, b and c According to the standard form of a quadratic equation, the value is found as compare both standard and question questions.
After comparing the equation we have a = 2, b = 12 and c = 8
Put the values of a, b, and c. You will get the value of x. The positive and negative sign shows two values of the single variables. 

                                                   = (-3±√80)
Now you have two values of x that is positive (-3+√80) and (-3-√80)
But it is the complex method to solve the equation and takes a lot of time to solve quadratic equations. If you need to solve these equations in the least time duration or within a minute, then use some tricks. The trick can help you to solve it in the least time.
First consider there some sign to get their answers.
If you have equation like
    ax² + bx + c= 0
    a+ bx -c= 0
    a- bx + c= 0
    a- bx –c =0 
Consider these signs to know their value signs.
First equation variable values include (-, -)
2nd includes (- , +)
3rd includes (+, +)
4th includes (+,-)
Consider an example to understand this trick to solve quadratic equations.
x²+5x-3=0
Now find the coefficient by multiplying x²and 3 coefficients.  2x3 may write as 6x1, and the result will be achieved by 6 and -1
The final root may divide by the 2 which is the x² coefficient. 
Now you have 6/2 and -1/2
You have roots (3, 0.5)
But the sign shows (-, +) and according to the trick you must have root (-3, 0.5)
This is a very short trick to get the root of unknown variables. The trick needs to only 30 to 60 seconds to solve quadratic equations. If you are looking the best method to solve quadratic problems in less than a minute then must apply this trick which requires least time.

Thursday, June 15, 2017

Basic Example for Solving Dividing Fractions for Kid

Mathematics makes man unique as compare to other, most of the experts advised kids or their parents to solve the mathematics to improve the brain capacity. More you solve the mathematics problem can make you genius. It has a lot of benefits to practicing numerical calculation in a daily manner. Mathematics has a huge number of forms and to understand all you have to spend a whole life. There is no need to know everything but necessary to know some essential part of the mathematics. Some important parts are aptitudes, numerical ability, and much more. The dividing fractions come under the numerical ability.
The numerical ability is one of the primary parts of mathematics which is used in the calculation and used in daily life. The dividing fraction is not a rigorous problem to solve but not so easy as seem. Sometimes, it posses the values which may not be divided by any number and sometimes it is really hard to simplify the problem.
Dividing fractions
Dividing fractions

For learner
If you are going to learn and complete your homework without any help, then a simple example can help. Consider an example and try to solve it. Try new questions every day, and you will learn easily to solve dividing fractions applications.

Dividing fractions
Dividing factors includes nominator and denominator. We have all seen the term arranged as 4/3. In this figure, the term 4 is called nominator, and 3 are referring to the denominator. In this figure 4 is divided by 3.
The application of dividing fraction is not as easy and difficult as. We can learn their applications with few examples.  Consider an example,
7/4÷21/8
The division of this figure creates complexity and difficult to solve. The easy method to solve this figure, change the sign between both numerical value. Keep the thing in mind that you can change the divide sign with multiplication and the positive sign with negative according to the mathematics rules. To solve this figure, you can replace the divide sign with multiplication but need to exchange nominator and denominator. This action balances the condition as previous. Basically, it is not a changing method but a trick to make easy the figure. After applying trick on it, it is easy to simplify the question get the result.
After changing the sign, you have the figure shown below
7/4×8/21
This figure is easy to solve. You have two choices to simplify the question that first is one, that eliminate the common part from nominator and denominator or another one is complex. Need to multiply nominator to nominator and same operation for the denominator.

From Method one-
You will get small figure that is 
7/4×8/21=2/3

Second method-
After applying the second method, you have
7/4×8/21=56/84
To simplify it, you need to eliminate common factors from both the sides. It will provide you the right answer.

56/84 = 2/3

Both the method provides the same answer, and there will be no variations. So you have the choice to select anyone. With the dividing fractions, you may know how to simplify the mathematics problems. More the practice of dividing fractions problem can make you perfect in few days.   

Saturday, June 10, 2017

How to Simplify the Linear Equations by a Simple Process?

Students have many difficulties in algebra and do not know how to solve algebraic equations. The equations are required to simplify to get the right answer. If you have any difficulty in the simplification of linear equations, you should know the simple process to simplify it. An easy process can bring a right solution of the problems on this topic quickly. To understand algebra, you should learn how to solve different types of algebraic equations. You should able to simplify algebraic equations and to find the value of a variable.

linear equations
linear equations

How to identify a linear equation?
Algebraic equations are used in many fields of mathematics. Linear equations are the algebraic equations which give a straight line on the graph. Basically, it has two variables, and if you plot a graph using the equation, you will obtain a straight line. There are so many different forms to write these algebraic equations. But most common form has variables like x or y and constants like 3 or 9 or c.

Case 1: some examples can help you to understand these equations as given below;
3y + 6 = 5x,
3( x + 1 ) = y – 2
x/2 = 3
5y – 6 = 0

Case 2: Normally, the variables do not have exponents or square and cube roots. Like x^2-2 = 0 and 4√y – x = 8
So, the equations listed in case 1 are the linear equations whereas in case 2 are not these equations. Now, you can easily find whether an algebraic equation is linear or not.
Here, a simple method to solve the problems of single variable linear equations is given. You can use this method for solving the equations that have a single variable.

The simple process to simplify the linear equation
·         Use the least common denominator to eliminate any fraction, if the equation has a fraction. Multiply both sides by the LCD to simply the equation.
·         Then, simplify the both sides of the linear equation. For the simplification, clear out the entire parenthesis and also combine the like terms.
·         The next step is just to put all the variables on one side and all the constants on another side of the equation.
·         The last step is to solve the both sides by addition or subtraction.
Here is an example following the above steps. You can see this example to get a good method for simplifying equations.
7(x – 2) + 21 = 6 x is the problem and solution is given below
7x- 14 + 21 = 6x
7x – 6x = 14 – 21
x= -7 is the right answer.

Many people do not verify the answer, but it is also important to verify the answer. This is very helpful you to identify that you have a right solution or not. It is useful to find your mistake. Put your answer in the original equation in the place of the variable (here, ‘x’) and then cross verify by solving it. There are so many other methods to simplify such equations. The substitution method is the method to solve the linear equations that have two variables. 

Thursday, June 1, 2017

Subtracting Fractions – How to Solve Such Fraction without any Mistake?

Fractions are the basics of mathematics, and thus it becomes necessary for you to explain fraction basics. Many students just hate fractions although they are easy as add numbers. So, today I am going to teach you basics and guide you as for how to use them? At first, we solve simple fractions and then a little harder one. So, let’s begin our “subtracting fractions” tutorial.

What do you need to know about solving denominators?
There are certain rules and things about fractions which are must be in your knowledge. Well, here we discuss essential so that you can be able to solve any fraction without mistakes.

        Always take care about zero number in the numerator. It’s a very common mistake that students do as they multiple zero with other digits. For example, 0/4 then its answer is zero and not 4. Yes, in the case of the reverse fraction, its solution is 4.
        Always consider signs as they are important and let you to the right answer if used correctly. Always remember that, (-,-)=(-), (+,+)=(+), (-,+)=(-) and (-,+)=(-). Learn it as you have to use it further in the equation.
        Always make the digits in dominator same while solving the equation. If they are equal already, then it is easy to solve but if not then make it same.  I know, this the toughest part of a fraction but it is easy as eating a pie.
        You should not have how to cancel number and have knowledge about common factors.  Students do it incorrectly and thus never get right answers while subtracting fractions.

Step to solve it
Let’s learn it by solving an example 3/4 – 6/12. Here we have taken simple examples, but you still got its concept. So, let’s continue it:

 Find the LCM of 4 and 12: remember what I have said earlier as make sure that denominators are the equal or of the same number. The LCM of them is twelve i.e. both of them are canceled by 4 & 3 which results in 12 when multiplied.

 Now cancel 4 & 12 by each other:  After finding LCM, you need to cancel four and twelve in the denominator by 4, and you will get 1 & 3.

Multiply 3 in the numerator by three by six by 1:   Here is the way to solve it: 3 x3 – 6 x 1/12 =3/12.  If you are confused here, then let me tell you that four are considered common number here.  4 is the only number which comes in the table of 4 &12. You have to choose a number which cancels both the number perfectly i.e. answers should not be in decimal. It should be a perfect number like 1, 2, 3……etc.

Last step: Now you need to solve 3/12 which answers to give 4. S, 4 is the answer to this equation and here its simplification completed.

Subtracting fractions are very easy, but you need to practice the steps to learn it. So, use the above steps and love solving fractions without getting wrong answers. 

Wednesday, May 24, 2017

Few Guidelines to set up and Solve Algebra Equations

Algebra has been one of the most important parts of mathematics since it was found. Studies in mathematics become more interesting with algebra. You need proper skills and tricks to be the master in algebra. You need to have a smart plan to be perfect in solving algebra equations. The most important part of learning this is being very clear with the basics. Perfect basics mean the perfect skills and answers to various problems. There are many easy ways to do this, however, some common tips would help the beginners in the best way. Therefore this content is focusing on some common tips to help you out with problems in algebra.


Some Common and useful tips for you  
Although there are many rules and guidelines to be learned and applied in algebraic problems you need a proper guide to use them in the right way. Here are some common points for you:

·         Read the problem properly:  Before you start solving the problem you need to read it well. You need to possess great patience while solving the problems in algebra. This will help you to recognize you the next step in the best manner. Rather than being in a hurry to get the answer, it is better to be slow and get the right answer. This is the most important step to notice all the operations and variables used in the equations.
·         Look out for keywords:  There are some keywords which guide you to know the operations and get the right way to setup the algebra equations. The various operations are indicated using some different words and blended into sentences. Here are some common words used for different operations: Addition- added to, combined, more than, etc. Subtraction uses words like the difference of, less than, etc. Therefore you need to lay stress on these terms to set up the equation in the correct form.
·         Underline the important: Anything you find important while solving the word problems should be underlined. This is one of the useful habits during solving algebra problems. This will help you to easily catch up the important factors in the question while setting up and solving the equations. Thus reading and marking the important points plays an important role in solving the algebraic problems.
·         Note down all the points mentioned in the problem: When you read the question, first note down the different factors you have recognized the problem. This will be the best way to set up the equation in a correct manner. This will also reduce the time taken in setting up and solving the equations. Double check what you have written so that there are even fewer chances of mistakes.
·         Practice and keep Practicing: Practice is the most important element in getting better with algebra. Regular practice can be the nested guide to lead you towards perfection.

Therefore these tips will surely help you to get the best in solving algebra equations. With few efforts and lots of practice, you will be the best in algebra.