Completing the square method

With the beginning of the topic Quadratic Equations I've reveal the method of solving quadratic equations, among those methods I've already explained Middle term splitting method and Quadratic Formula now it's the time to introduce one more method to get rid of typical Quadratic equations.

Completing the square method

1. What Completing the square method method is all about  ?

This is a process to find roots of any Quadratic equation by making squares, this can be understood more briefly with an example.

This is more explainable with following image:

2. Why is there need to have this method ?

   A good question, instead..!!

Sometimes this finds to be difficult to evaluate roots of any Quadratic Equations by MTS in this situation we tend to look at Quadratic Formula.

   But in most of the situation we would be facing some hectic calculations, to avoid such things we must have to look at another method. This need arose the concept of completing the square method.

3. How this method works ?

let's have a Quadratic equation i.e.

ax² + bx + c = 0

this can be done within five steps :

• Step 1 Divide all terms by a (the coefficient of x²).

i.e.  x² + (b/a)x + (c/a) = 0

• Step 2 Move the number term (c/a) to the right side of the equation.

i.e.  x² + (b/a)x = - (c/a) 

• Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation. i.e. to complete the square we need to add (b/2a) in left side and to balance the equation the same should be done in right side

x² + (b/a)x +(b/2a)² =(c/a) +(b/2a)²

now this can be written as

[x + (b/2a)]² = c/a + (b/2a)²

• Step 4 Take the square root on both sides of the equation.

• Step 5 Subtract the number that remains on the left side of the equation to find x.

for practically​ understanding see an example below for equation: 

x² - 10x + 16 = 0

I hope you enjoyed the topic and all the methods for obtaining Solutions of Quadratic equations. Feel free to share.