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