completing the square?

Question

solve the following equations by completing the square x^2+2x-3=0.

Answer 1

Given equation x^2+2x-3 = 0

For completing squre we able to write -3 = -4+1

x^2+2x+1-4 = 0

Add 4 to each side.

x^2+2x+1 = 4

(x+1)^2 = 4

Apply squre root on each side.

x+1 = ±2

x = 2-1 and x = -2-1

x = 1 and x = -3

Solution x = 1,-3.

Answer 2

The equation is x² + 2x - 3 = 0.

Separate variables and constants aside by adding 3 to each side.

x² + 2x = 3.

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 2. so, (half the x coefficient)² = (2/2)²= 1.

Add 1 to each side.

x² + 2x + 1 = 3 + 1

(x + 1)² = 4

(x + 1)² = (± 2)²

x + 1 = ± 2

x = - 1 + 2 and x = - 1 - 2

x = 1 and x = - 3.

The solutions are x = 1 and x = - 3.