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Simplifying 2k2 = -2k + 112 Reorder the terms: 2k2 = 112 + -2k Solving 2k2 = 112 + -2k Solving for variable 'k'. Reorder the terms: -112 + 2k + 2k2 = 112 + -2k + -112 + 2k Reorder the terms: -112 + 2k + 2k2 = 112 + -112 + -2k + 2k Combine like terms: 112 + -112 = 0 -112 + 2k + 2k2 = 0 + -2k + 2k -112 + 2k + 2k2 = -2k + 2k Combine like terms: -2k + 2k = 0 -112 + 2k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + k + k2) = 0 Factor a trinomial. 2((-8 + -1k)(7 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1k)' equal to zero and attempt to solve: Simplifying -8 + -1k = 0 Solving -8 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1k = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1k = 0 + 8 -1k = 0 + 8 Combine like terms: 0 + 8 = 8 -1k = 8 Divide each side by '-1'. k = -8 Simplifying k = -8Subproblem 2
Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 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 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Solution
k = {-8, 7}
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