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Simplifying (-1k + 4)(-2k + -9) = 0 Reorder the terms: (4 + -1k)(-2k + -9) = 0 Reorder the terms: (4 + -1k)(-9 + -2k) = 0 Multiply (4 + -1k) * (-9 + -2k) (4(-9 + -2k) + -1k * (-9 + -2k)) = 0 ((-9 * 4 + -2k * 4) + -1k * (-9 + -2k)) = 0 ((-36 + -8k) + -1k * (-9 + -2k)) = 0 (-36 + -8k + (-9 * -1k + -2k * -1k)) = 0 (-36 + -8k + (9k + 2k2)) = 0 Combine like terms: -8k + 9k = 1k (-36 + 1k + 2k2) = 0 Solving -36 + 1k + 2k2 = 0 Solving for variable 'k'. Factor a trinomial. (-9 + -2k)(4 + -1k) = 0Subproblem 1
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 = -4.5Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {-4.5, 4}
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