**2.2b Solving Quadratic Equations – Completing the Square (Examples)**

**(A) Steps to solve quadratic equation using completing the square**

**• make sure that the coefficient of**

*x*is 1.

• Rewrite the equation

*ax*

^{2 }+

*bx*+

*c*= 0 in the form

*ax*

^{2 }+

*bx*= –

*c.*

• Add ${\left(\frac{\text{coefficientof}x}{2}\right)}^{2}$ to both side of the equation.

**Example**

**:**

Solve the following quadratic equations by completing the square.

(a)

(a)

*x*^{2}– 6*x*– 3 = 0(b) 2

*x*^{2}– 5*x*– 7 = 0(c)

*x*^{2}+ 1 = 10*x***/**3

*Solution:*