Answer:(x + 9)² = 49 has the same solution as equation x² + 18x + 32 = 0.
Explanation:
Given : An equation : x^2 + 18x + 32 = 0.
To find : Which equation has the same solutions as the equation .
Solution : We have x^2 + 18x + 32 = 0.
By factoring : x^2 + 16x +2x+ 32 = 0.
Taking common x( x+16) +2(x+16) =0.
By grouping : (x+2) (x+16) =0.
x = -2 , x = -16 .
(x + 9)² = 49
By square formula (a+b)²
x² + 81 + 18x =49.
On subtracting by 49 both side
x² + 81 + 18x -49 =49-49.
x² + 18x + 32 = 0.
Therefore, (x + 9)² = 49 has the same solution as equation x² + 18x + 32 = 0.