x 2 + 10 x + 25 = 9 ( ∗ ) x 2 + 2 x ⋅ 5 + 5 2 = 9 ( x + 5 ) 2 = 9 ⟺ x + 5 = 3 or x + 5 = − 3 x = 3 − 5 or x = − 5 − 3 x = − 2 or x = − 8 ← so l u t i o n s
( ∗ ) ( a + b ) 2 = a 2 + 2 ab + b 2
o t h er m e t h o d e : x 2 + 10 x + 25 = 9 x 2 + 10 x + 25 − 9 = 0 x 2 + 10 x + 16 = 0 x 2 + 2 x + 8 x + 16 = 0 x ( x + 2 ) + 8 ( x + 2 ) = 0 ( x + 2 ) ( x + 8 ) = 0 ⟺ x + 2 = 0 or x + 8 = 0 x = − 2 or x = − 8
x 2 + 10 x + 25 = 9 ( x + 5 ) 2 = 9 x + 5 = 3 ∨ x + 5 = − 3 x = − 2 ∨ x = − 8
The solutions to the equation x 2 + 10 x + 25 = 9 are x = − 2 and x = − 8 . Both solutions were verified by substituting them back into the original equation. Hence, the answer is x = − 2 or x = − 8 .
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