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Simplifying (k + 4)(k + -7) = 0 Reorder the terms: (4 + k)(k + -7) = 0 Reorder the terms: (4 + k)(-7 + k) = 0 Multiply (4 + k) * (-7 + k) (4(-7 + k) + k(-7 + k)) = 0 ((-7 * 4 + k * 4) + k(-7 + k)) = 0 ((-28 + 4k) + k(-7 + k)) = 0 (-28 + 4k + (-7 * k + k * k)) = 0 (-28 + 4k + (-7k + k2)) = 0 Combine like terms: 4k + -7k = -3k (-28 + -3k + k2) = 0 Solving -28 + -3k + k2 = 0 Solving for variable 'k'. Factor a trinomial. (-4 + -1k)(7 + -1k) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Solution
k = {-4, 7}
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