Question

18. Solve x^2+ 6x - 16 = 0 by completing the square.
Please give detailed steps!!

Answer 1

x1 = -8, x2= 2

Explanation:

1. Write 6x as a difference

= x^2 + 8x - 2x - 16 = 0

2. Factor the expressions

= x ( x + 8 ) - 2x - 16 = 0

= x ( x + 8 ) - 2 ( x + 8 ) = 0

Factor out x + 8 from the expression

= ( x + 8 ) ( x - 2 ) = 0

3. When the product of factors = 0, at least one factor is 0

x + 8 = 0

x - 2 = 0

4. Solve the equation for x

x = - 8

x = 2

Therefore, the equation has 2 solutions :

x1 = -8, x2 = 2