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Simplifying 120 = -16x2 + 96x + 12 Reorder the terms: 120 = 12 + 96x + -16x2 Solving 120 = 12 + 96x + -16x2 Solving for variable 'x'. Combine like terms: 120 + -12 = 108 108 + -96x + 16x2 = 12 + 96x + -16x2 + -12 + -96x + 16x2 Reorder the terms: 108 + -96x + 16x2 = 12 + -12 + 96x + -96x + -16x2 + 16x2 Combine like terms: 12 + -12 = 0 108 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 108 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 108 + -96x + 16x2 = 0 + -16x2 + 16x2 108 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 108 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(27 + -24x + 4x2) = 0 Factor a trinomial. 4((3 + -2x)(9 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {1.5, 4.5}
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