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Simplifying 15k2 = 25 + -10k Solving 15k2 = 25 + -10k Solving for variable 'k'. Reorder the terms: -25 + 10k + 15k2 = 25 + -10k + -25 + 10k Reorder the terms: -25 + 10k + 15k2 = 25 + -25 + -10k + 10k Combine like terms: 25 + -25 = 0 -25 + 10k + 15k2 = 0 + -10k + 10k -25 + 10k + 15k2 = -10k + 10k Combine like terms: -10k + 10k = 0 -25 + 10k + 15k2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + 2k + 3k2) = 0 Factor a trinomial. 5((-5 + -3k)(1 + -1k)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -3k)' equal to zero and attempt to solve: Simplifying -5 + -3k = 0 Solving -5 + -3k = 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 + -3k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3k = 0 + 5 -3k = 0 + 5 Combine like terms: 0 + 5 = 5 -3k = 5 Divide each side by '-3'. k = -1.666666667 Simplifying k = -1.666666667Subproblem 2
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 = 1Solution
k = {-1.666666667, 1}
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