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Simplifying 4k2 + -4k + 1 = 9 Reorder the terms: 1 + -4k + 4k2 = 9 Solving 1 + -4k + 4k2 = 9 Solving for variable 'k'. Reorder the terms: 1 + -9 + -4k + 4k2 = 9 + -9 Combine like terms: 1 + -9 = -8 -8 + -4k + 4k2 = 9 + -9 Combine like terms: 9 + -9 = 0 -8 + -4k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -1k + k2) = 0 Factor a trinomial. 4((-1 + -1k)(2 + -1k)) = 0 Ignore the factor 4.Subproblem 1
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 = -1Subproblem 2
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 = 2Solution
k = {-1, 2}
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