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Simplifying k2 + 16k + 71 = 8 Reorder the terms: 71 + 16k + k2 = 8 Solving 71 + 16k + k2 = 8 Solving for variable 'k'. Reorder the terms: 71 + -8 + 16k + k2 = 8 + -8 Combine like terms: 71 + -8 = 63 63 + 16k + k2 = 8 + -8 Combine like terms: 8 + -8 = 0 63 + 16k + k2 = 0 Factor a trinomial. (9 + k)(7 + k) = 0Subproblem 1
Set the factor '(9 + k)' equal to zero and attempt to solve: Simplifying 9 + k = 0 Solving 9 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + k = 0 + -9 k = 0 + -9 Combine like terms: 0 + -9 = -9 k = -9 Simplifying k = -9Subproblem 2
Set the factor '(7 + k)' equal to zero and attempt to solve: Simplifying 7 + k = 0 Solving 7 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + k = 0 + -7 k = 0 + -7 Combine like terms: 0 + -7 = -7 k = -7 Simplifying k = -7Solution
k = {-9, -7}
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