what number would you add to the equation below to complete the square x^2 + 8x = 9

Question

this is a complete square problem.

Answer 1

Given equation x^2+8x = 9

Subtract 9 from each side.

x^2+8x-9 = 9-9

x^2+8x-9 = 0

To complete the squre add 25 to each side.

x^2+8x-9+25 = 0+25

x^2+8x+16 = 25

(x+4)^2 = 25

Apply squre root on each side.

x+4 = ±5

x+4 = 5 and x+4 = -5

Subtract 4 from each side.

x+4-4 = 5-4 and x+4-4 = -5-4

x = 1 and x = -9

Solution x = 1,-9.

Answer 2

The equation is x² + 8x = 9.

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 = 9 + 16

(x + 4)² = 25.

So, 16 is add to the equation x² + 8x = 9 to complete the square.