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Simplifying k2 = -4k + 21 Reorder the terms: k2 = 21 + -4k Solving k2 = 21 + -4k Solving for variable 'k'. Reorder the terms: -21 + 4k + k2 = 21 + -4k + -21 + 4k Reorder the terms: -21 + 4k + k2 = 21 + -21 + -4k + 4k Combine like terms: 21 + -21 = 0 -21 + 4k + k2 = 0 + -4k + 4k -21 + 4k + k2 = -4k + 4k Combine like terms: -4k + 4k = 0 -21 + 4k + k2 = 0 Factor a trinomial. (-7 + -1k)(3 + -1k) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {-7, 3}
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