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Simplifying 18k2 + -32 = 2k2 + -56k Reorder the terms: -32 + 18k2 = 2k2 + -56k Reorder the terms: -32 + 18k2 = -56k + 2k2 Solving -32 + 18k2 = -56k + 2k2 Solving for variable 'k'. Reorder the terms: -32 + 56k + 18k2 + -2k2 = -56k + 2k2 + 56k + -2k2 Combine like terms: 18k2 + -2k2 = 16k2 -32 + 56k + 16k2 = -56k + 2k2 + 56k + -2k2 Reorder the terms: -32 + 56k + 16k2 = -56k + 56k + 2k2 + -2k2 Combine like terms: -56k + 56k = 0 -32 + 56k + 16k2 = 0 + 2k2 + -2k2 -32 + 56k + 16k2 = 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 -32 + 56k + 16k2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-4 + 7k + 2k2) = 0 Factor a trinomial. 8((-4 + -1k)(1 + -2k)) = 0 Ignore the factor 8.Subproblem 1
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 = -4Subproblem 2
Set the factor '(1 + -2k)' equal to zero and attempt to solve: Simplifying 1 + -2k = 0 Solving 1 + -2k = 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 + -2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2k = 0 + -1 -2k = 0 + -1 Combine like terms: 0 + -1 = -1 -2k = -1 Divide each side by '-2'. k = 0.5 Simplifying k = 0.5Solution
k = {-4, 0.5}
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