how do you solve the following by using complete square x^2+8x+9=32?

Question

help please!

Answer 1

Given equation x^2+8x+9 = 32

For complete the square add 7 to each side.

x^2+8x+9+7 = 32+7

x^2+8x+16 = 39

(x+4)^2 = 39

Apply squre root on each side.

√(x+4)^2 = √39

x+4 = √39

Subtract 4 from each side.

x+4-4 = √39 -4

Solution x = √39 -4.

Comments

The solution of the equation is x = - 4 + √39 and x = - 4 - √39.

Answer 2

The equation is x² + 8x + 9 = 32.

Separate variables and constants aside by subtracting 9 from each side.

x² + 8x = 32 - 9 = 23

x² + 8x = 23.

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

 Here x coefficient = 8. so, (half the x coefficient)² = (8/2)²= 16.

Add 16 to each side.

x² + 8x + 16 = 23 + 16

(x + 4)² = 39

(x + 4)² = (± √39)²

x + 4 = ± √39

x = - 4 + √39 and x = - 4 - √39.

The solutions are x = - 4 + √39 and x = - 4 - √39.