STEP 1: Recall what is a quadratic equation

https://study.com/academy/lesson/what-is-a-quadratic-equation-definition-examples.html

STEP 2: Solve the quadratic by completing the square

For example take a quadratic equation 4x^{2} + 8x + 1= 0

Divide the complete equation by the coefficient of x^{2} which is 4

\frac{4x^{2}}{4} +\frac{8}{4}x + \frac{1}{4} = 0

Now move the constant term to the right hand side of the equation

x^{2} +\frac{8}{4}x = \frac{-1}{4}

x^{2} +2x = -\frac{-1}{4}

Adding 1 on both sides

x^{2} + 2x + 1 = -\frac{-1}{4} + 1

STEP 3:

Recall the (a+b)^{2} formula

https://www.youtube.com/watch?v=Ygkzh4sJOQE

Applying this on x^{2} + 2x + 1 we get

(x+1)^{2} = \frac{3}{4}

(x+1) = \pm\sqrt\frac{3}{4}

x+1 = \pm\frac{\sqrt{3}}{2}

STEP 4:

Recall how to isolate the x variable

https://www.youtube.com/watch?v=TX2ZEXDeRgU

Isolate the x variable

x = -1 +\frac{\sqrt{3}}{2}

and

x = -1 -\frac{\sqrt{3}}{2}

This is how we solve a quadratic by completing the square.