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Simplifying 5k2 + -13 + 6k + -2k2 + -16k = 0 Reorder the terms: -13 + 6k + -16k + 5k2 + -2k2 = 0 Combine like terms: 6k + -16k = -10k -13 + -10k + 5k2 + -2k2 = 0 Combine like terms: 5k2 + -2k2 = 3k2 -13 + -10k + 3k2 = 0 Solving -13 + -10k + 3k2 = 0 Solving for variable 'k'. Factor a trinomial. (-1 + -1k)(13 + -3k) = 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 '(13 + -3k)' equal to zero and attempt to solve: Simplifying 13 + -3k = 0 Solving 13 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3k = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3k = 0 + -13 -3k = 0 + -13 Combine like terms: 0 + -13 = -13 -3k = -13 Divide each side by '-3'. k = 4.333333333 Simplifying k = 4.333333333Solution
k = {-1, 4.333333333}
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