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Simplifying 8k2 + -1k + -135 = 2k2 + -4k Reorder the terms: -135 + -1k + 8k2 = 2k2 + -4k Reorder the terms: -135 + -1k + 8k2 = -4k + 2k2 Solving -135 + -1k + 8k2 = -4k + 2k2 Solving for variable 'k'. Reorder the terms: -135 + -1k + 4k + 8k2 + -2k2 = -4k + 2k2 + 4k + -2k2 Combine like terms: -1k + 4k = 3k -135 + 3k + 8k2 + -2k2 = -4k + 2k2 + 4k + -2k2 Combine like terms: 8k2 + -2k2 = 6k2 -135 + 3k + 6k2 = -4k + 2k2 + 4k + -2k2 Reorder the terms: -135 + 3k + 6k2 = -4k + 4k + 2k2 + -2k2 Combine like terms: -4k + 4k = 0 -135 + 3k + 6k2 = 0 + 2k2 + -2k2 -135 + 3k + 6k2 = 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 -135 + 3k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-45 + k + 2k2) = 0 Factor a trinomial. 3((-5 + -1k)(9 + -2k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1k)' equal to zero and attempt to solve: Simplifying -5 + -1k = 0 Solving -5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1k = 0 + 5 -1k = 0 + 5 Combine like terms: 0 + 5 = 5 -1k = 5 Divide each side by '-1'. k = -5 Simplifying k = -5Subproblem 2
Set the factor '(9 + -2k)' equal to zero and attempt to solve: Simplifying 9 + -2k = 0 Solving 9 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2k = 0 + -9 -2k = 0 + -9 Combine like terms: 0 + -9 = -9 -2k = -9 Divide each side by '-2'. k = 4.5 Simplifying k = 4.5Solution
k = {-5, 4.5}
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