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Simplifying 4k2 + -2(-1k + 12) = 86 Reorder the terms: 4k2 + -2(12 + -1k) = 86 4k2 + (12 * -2 + -1k * -2) = 86 4k2 + (-24 + 2k) = 86 Reorder the terms: -24 + 2k + 4k2 = 86 Solving -24 + 2k + 4k2 = 86 Solving for variable 'k'. Reorder the terms: -24 + -86 + 2k + 4k2 = 86 + -86 Combine like terms: -24 + -86 = -110 -110 + 2k + 4k2 = 86 + -86 Combine like terms: 86 + -86 = 0 -110 + 2k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + k + 2k2) = 0 Factor a trinomial. 2((-11 + -2k)(5 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -2k)' equal to zero and attempt to solve: Simplifying -11 + -2k = 0 Solving -11 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2k = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2k = 0 + 11 -2k = 0 + 11 Combine like terms: 0 + 11 = 11 -2k = 11 Divide each side by '-2'. k = -5.5 Simplifying k = -5.5Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5Solution
k = {-5.5, 5}
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