Answer:
see explanation
Step-by-step explanation:
Given
x² + 10x + 14 = - 7 ( subtract 14 from both sides )
x² + 10x = - 21
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(5)x + 25 = - 21 + 25
(x + 5)² = 4 ( take the square root of both sides )
x + 5 = ± 2 ( subtract 5 from both sides )
x = - 5 ± 2
x = - 5 - 2 = - 7, or x = - 5 + 2 = - 3
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The equation can also be solved by factoring
x² + 10x + 14 = - 7 ( add 7 to both sides )
x² + 10x + 21 = 0 ← in standard form
(x + 7)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x + 3 = 0 ⇒ x = - 3
