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Simplifying -16x2 + 80x + 32 = 132 Reorder the terms: 32 + 80x + -16x2 = 132 Solving 32 + 80x + -16x2 = 132 Solving for variable 'x'. Reorder the terms: 32 + -132 + 80x + -16x2 = 132 + -132 Combine like terms: 32 + -132 = -100 -100 + 80x + -16x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -100 + 80x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 20x + -4x2) = 0 Factor a trinomial. 4((-5 + 2x)(5 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {2.5, 2.5}
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