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Simplifying 10k2 + -100 = 15k Reorder the terms: -100 + 10k2 = 15k Solving -100 + 10k2 = 15k Solving for variable 'k'. Reorder the terms: -100 + -15k + 10k2 = 15k + -15k Combine like terms: 15k + -15k = 0 -100 + -15k + 10k2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + -3k + 2k2) = 0 Factor a trinomial. 5((-5 + -2k)(4 + -1k)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -2k)' equal to zero and attempt to solve: Simplifying -5 + -2k = 0 Solving -5 + -2k = 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 + -2k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2k = 0 + 5 -2k = 0 + 5 Combine like terms: 0 + 5 = 5 -2k = 5 Divide each side by '-2'. k = -2.5 Simplifying k = -2.5Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 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 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {-2.5, 4}
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