Question

x^2+2x-14=10 by completing the square.

Answer 1

Given equation x^2+2x-14 = 10

To complete square we can able to write -14 = 1-15

x^2+2x+1-15 = 10

Add 15 to each side.

x^2+2x+1-15+15 = 10+15

(x+1)^2 = 25

Apply squre root on each side.

√(x+1)^2 = √25

x+1 = ±5

x+1 = 5 and x+1 = -5

Subtract 1from each side.

x+1-1 = 5-1 and x+1-1 = -5-1

x = 4 and x = -6

Solution x = 4,-6.

Answer 2

The equation is x² + 2x - 14 = 10.

Separate variables and constants aside by adding 14 to each side.

x² + 2x = 10 + 14 = 24

x² + 2x = 24.

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 = 24 + 1

(x + 1)² = 25

(x + 1)² = (± 5)²

x + 1 = ± 5

x = - 1 + 5 and x = - 1 - 5.

The solutions are x =  4 and x = - 6.