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

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.

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

    ax²+ bx -c= 0

    ax²- bx + c= 0

    ax²- 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.