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Simplifying -20k = -2(16k + -8) * 16k Reorder the terms: -20k = -2(-8 + 16k) * 16k Reorder the terms for easier multiplication: -20k = -2 * 16k(-8 + 16k) Multiply -2 * 16 -20k = -32k(-8 + 16k) -20k = (-8 * -32k + 16k * -32k) -20k = (256k + -512k2) Solving -20k = 256k + -512k2 Solving for variable 'k'. Combine like terms: -20k + -256k = -276k -276k + 512k2 = 256k + -512k2 + -256k + 512k2 Reorder the terms: -276k + 512k2 = 256k + -256k + -512k2 + 512k2 Combine like terms: 256k + -256k = 0 -276k + 512k2 = 0 + -512k2 + 512k2 -276k + 512k2 = -512k2 + 512k2 Combine like terms: -512k2 + 512k2 = 0 -276k + 512k2 = 0 Factor out the Greatest Common Factor (GCF), '4k'. 4k(-69 + 128k) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(-69 + 128k)' equal to zero and attempt to solve: Simplifying -69 + 128k = 0 Solving -69 + 128k = 0 Move all terms containing k to the left, all other terms to the right. Add '69' to each side of the equation. -69 + 69 + 128k = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 128k = 0 + 69 128k = 0 + 69 Combine like terms: 0 + 69 = 69 128k = 69 Divide each side by '128'. k = 0.5390625 Simplifying k = 0.5390625Solution
k = {0, 0.5390625}
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