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Simplifying 0 = 3k2 + -10k + 8 Reorder the terms: 0 = 8 + -10k + 3k2 Solving 0 = 8 + -10k + 3k2 Solving for variable 'k'. Combine like terms: 0 + -8 = -8 -8 + 10k + -3k2 = 8 + -10k + 3k2 + -8 + 10k + -3k2 Reorder the terms: -8 + 10k + -3k2 = 8 + -8 + -10k + 10k + 3k2 + -3k2 Combine like terms: 8 + -8 = 0 -8 + 10k + -3k2 = 0 + -10k + 10k + 3k2 + -3k2 -8 + 10k + -3k2 = -10k + 10k + 3k2 + -3k2 Combine like terms: -10k + 10k = 0 -8 + 10k + -3k2 = 0 + 3k2 + -3k2 -8 + 10k + -3k2 = 3k2 + -3k2 Combine like terms: 3k2 + -3k2 = 0 -8 + 10k + -3k2 = 0 Factor a trinomial. (-2 + k)(4 + -3k) = 0Subproblem 1
Set the factor '(-2 + k)' equal to zero and attempt to solve: Simplifying -2 + k = 0 Solving -2 + k = 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 + k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + k = 0 + 2 k = 0 + 2 Combine like terms: 0 + 2 = 2 k = 2 Simplifying k = 2Subproblem 2
Set the factor '(4 + -3k)' equal to zero and attempt to solve: Simplifying 4 + -3k = 0 Solving 4 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3k = 0 + -4 -3k = 0 + -4 Combine like terms: 0 + -4 = -4 -3k = -4 Divide each side by '-3'. k = 1.333333333 Simplifying k = 1.333333333Solution
k = {2, 1.333333333}
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