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Simplifying 24x2 = -66x + 120 Reorder the terms: 24x2 = 120 + -66x Solving 24x2 = 120 + -66x Solving for variable 'x'. Reorder the terms: -120 + 66x + 24x2 = 120 + -66x + -120 + 66x Reorder the terms: -120 + 66x + 24x2 = 120 + -120 + -66x + 66x Combine like terms: 120 + -120 = 0 -120 + 66x + 24x2 = 0 + -66x + 66x -120 + 66x + 24x2 = -66x + 66x Combine like terms: -66x + 66x = 0 -120 + 66x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-20 + 11x + 4x2) = 0 Factor a trinomial. 6((-4 + -1x)(5 + -4x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Solution
x = {-4, 1.25}
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