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Simplifying 4k2 = 40k + 44 Reorder the terms: 4k2 = 44 + 40k Solving 4k2 = 44 + 40k Solving for variable 'k'. Reorder the terms: -44 + -40k + 4k2 = 44 + 40k + -44 + -40k Reorder the terms: -44 + -40k + 4k2 = 44 + -44 + 40k + -40k Combine like terms: 44 + -44 = 0 -44 + -40k + 4k2 = 0 + 40k + -40k -44 + -40k + 4k2 = 40k + -40k Combine like terms: 40k + -40k = 0 -44 + -40k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + -10k + k2) = 0 Factor a trinomial. 4((-1 + -1k)(11 + -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 '(11 + -1k)' equal to zero and attempt to solve: Simplifying 11 + -1k = 0 Solving 11 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1k = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1k = 0 + -11 -1k = 0 + -11 Combine like terms: 0 + -11 = -11 -1k = -11 Divide each side by '-1'. k = 11 Simplifying k = 11Solution
k = {-1, 11}
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