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Simplifying k2 = 13k + -40 Reorder the terms: k2 = -40 + 13k Solving k2 = -40 + 13k Solving for variable 'k'. Reorder the terms: 40 + -13k + k2 = -40 + 13k + 40 + -13k Reorder the terms: 40 + -13k + k2 = -40 + 40 + 13k + -13k Combine like terms: -40 + 40 = 0 40 + -13k + k2 = 0 + 13k + -13k 40 + -13k + k2 = 13k + -13k Combine like terms: 13k + -13k = 0 40 + -13k + k2 = 0 Factor a trinomial. (5 + -1k)(8 + -1k) = 0Subproblem 1
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 = 5Subproblem 2
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 = 8Solution
k = {5, 8}
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