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Simplifying 5k + -20 = k2 + -4k + -6 Reorder the terms: -20 + 5k = k2 + -4k + -6 Reorder the terms: -20 + 5k = -6 + -4k + k2 Solving -20 + 5k = -6 + -4k + k2 Solving for variable 'k'. Reorder the terms: -20 + 6 + 5k + 4k + -1k2 = -6 + -4k + k2 + 6 + 4k + -1k2 Combine like terms: -20 + 6 = -14 -14 + 5k + 4k + -1k2 = -6 + -4k + k2 + 6 + 4k + -1k2 Combine like terms: 5k + 4k = 9k -14 + 9k + -1k2 = -6 + -4k + k2 + 6 + 4k + -1k2 Reorder the terms: -14 + 9k + -1k2 = -6 + 6 + -4k + 4k + k2 + -1k2 Combine like terms: -6 + 6 = 0 -14 + 9k + -1k2 = 0 + -4k + 4k + k2 + -1k2 -14 + 9k + -1k2 = -4k + 4k + k2 + -1k2 Combine like terms: -4k + 4k = 0 -14 + 9k + -1k2 = 0 + k2 + -1k2 -14 + 9k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -14 + 9k + -1k2 = 0 Factor a trinomial. (-7 + k)(2 + -1k) = 0Subproblem 1
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 = 7Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Solution
k = {7, 2}
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