# How to solve Quadratic Equation By Completing The Square Method

QUADRATIC EQUATION BY COMPLETING THE SQUARE METHOD

At some point it is difficult to solve some quadratic equation by factorization some expression is even impossible to factorize, in such case you switch to completing the square method.

To find the roots of a quadratic equation in the form:

\{a}{x}^{2}+{b}{x}+{c}={0}ax2+bx+c=0,

(i) If a does not equal \{1}1, divide each side by a (so that the coefficient of the x2 is \{1}1).

(ii) Rewrite the equation with the constant term on the right side.

(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.

To find the roots of a quadratic equation in the form:

\{a}{x}^{2}+{b}{x}+{c}={0}ax2+bx+c=0,

(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).

(ii) Rewrite the equation with the constant term on the right side.

(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.

Consider   2X2   –   11x    +   12   =   0

Step1

Separate the constant and variable containing elements into different sides of the equality sign

2X2   –   11x    =   -12

Step2

Divide both side by the coefficient of  x2

X2   –    x  =  -6

Step3

Add  the square of half of the coefficient of  x  to both side of the  equation

X   –    x  +  (-)2   =  -6  +

(x  –  )2  –

(x  –  )2

Taking the square root of both sides

X  –     = ±

X  =    ±

X =   and  x  =

X  =    and  x  =

X  =4    and  x  =

The following must be noted whenever completing the square method is use

The coefficient of  x2   must be reduce to 1

The constant (value independent on x must be moved to the right hand side of the equation.

Every quadratic equation must have two roots either unique or the same

So now try your hands on this one  3X2   –   13x    +   10   =   0

Answer is   and 1