# Solving Quadratic Equations by Completing the Square

An interesting method for solving quadratic equations came from India. The steps are:

(a) Move the constant term to the right side of the equation

(b) Multiply each term in the equation by four times the coefficient of the x2 term.

(c) Square the coefficient of the original x term and add it to both sides of the equation.

(d) Take the square root of both sides

(e) Set the left side of the equation equal to the positive square root of both sides.

(f) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x.

(g) Set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for x.

Explain the Examples below:

1)x2- 2x-3=0

2)4x2 -4x-3=0

3)X2=12x-64=0

4)2x2-3x-5=0

#### Solution Preview

... = -2

x = 1 - 2 = -1

(B) 4x^2 - 4x = -3

16x^2 - 16x = -12

16x^2 - 16x + 64 = 52

(4x - 8)^2 = 52

4x - 8 = (sqrt)52 = (plus or minus) 2 (sqrt)13

4x = 8 + 2 (sqrt)13

x = 2 + ...