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Simplifying 5x2 + -44x + 120 = -30 + 11x Reorder the terms: 120 + -44x + 5x2 = -30 + 11x Solving 120 + -44x + 5x2 = -30 + 11x Solving for variable 'x'. Reorder the terms: 120 + 30 + -44x + -11x + 5x2 = -30 + 11x + 30 + -11x Combine like terms: 120 + 30 = 150 150 + -44x + -11x + 5x2 = -30 + 11x + 30 + -11x Combine like terms: -44x + -11x = -55x 150 + -55x + 5x2 = -30 + 11x + 30 + -11x Reorder the terms: 150 + -55x + 5x2 = -30 + 30 + 11x + -11x Combine like terms: -30 + 30 = 0 150 + -55x + 5x2 = 0 + 11x + -11x 150 + -55x + 5x2 = 11x + -11x Combine like terms: 11x + -11x = 0 150 + -55x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(30 + -11x + x2) = 0 Factor a trinomial. 5((5 + -1x)(6 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {5, 6}
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