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what are the solutions to (x+7)^2 = 81

1 answer

To solve this equation, we need to expand the left side of the equation and then solve for x.

1. Expand the left side of the equation:
(x + 7)^2 = 81
(x + 7)(x + 7) = 81
x^2 + 14x + 49 = 81

2. Subtract 81 from both sides of the equation:
x^2 + 14x + 49 - 81 = 0
x^2 + 14x - 32 = 0

3. Factor the quadratic equation:
(x + 16)(x - 2) = 0

4. Set each factor equal to zero and solve for x:
x + 16 = 0
x = -16

x - 2 = 0
x = 2

Therefore, the solutions to the equation (x + 7)^2 = 81 are x = -16 and x = 2.
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