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Simplifying 16k2 + 16k + 4 + -28 + 4k = 0 Reorder the terms: 4 + -28 + 16k + 4k + 16k2 = 0 Combine like terms: 4 + -28 = -24 -24 + 16k + 4k + 16k2 = 0 Combine like terms: 16k + 4k = 20k -24 + 20k + 16k2 = 0 Solving -24 + 20k + 16k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 5k + 4k2) = 0 Factor a trinomial. 4((-2 + -1k)(3 + -4k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 2
Set the factor '(3 + -4k)' equal to zero and attempt to solve: Simplifying 3 + -4k = 0 Solving 3 + -4k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4k = 0 + -3 -4k = 0 + -3 Combine like terms: 0 + -3 = -3 -4k = -3 Divide each side by '-4'. k = 0.75 Simplifying k = 0.75Solution
k = {-2, 0.75}
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