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Simplifying k2 = 4k + 12 Reorder the terms: k2 = 12 + 4k Solving k2 = 12 + 4k Solving for variable 'k'. Reorder the terms: -12 + -4k + k2 = 12 + 4k + -12 + -4k Reorder the terms: -12 + -4k + k2 = 12 + -12 + 4k + -4k Combine like terms: 12 + -12 = 0 -12 + -4k + k2 = 0 + 4k + -4k -12 + -4k + k2 = 4k + -4k Combine like terms: 4k + -4k = 0 -12 + -4k + k2 = 0 Factor a trinomial. (-2 + -1k)(6 + -1k) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve: Simplifying 6 + -1k = 0 Solving 6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1k = 0 + -6 -1k = 0 + -6 Combine like terms: 0 + -6 = -6 -1k = -6 Divide each side by '-1'. k = 6 Simplifying k = 6Solution
k = {-2, 6}
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