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Simplifying 0 = -16x2 + 48x + 160 Reorder the terms: 0 = 160 + 48x + -16x2 Solving 0 = 160 + 48x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -160 = -160 -160 + -48x + 16x2 = 160 + 48x + -16x2 + -160 + -48x + 16x2 Reorder the terms: -160 + -48x + 16x2 = 160 + -160 + 48x + -48x + -16x2 + 16x2 Combine like terms: 160 + -160 = 0 -160 + -48x + 16x2 = 0 + 48x + -48x + -16x2 + 16x2 -160 + -48x + 16x2 = 48x + -48x + -16x2 + 16x2 Combine like terms: 48x + -48x = 0 -160 + -48x + 16x2 = 0 + -16x2 + 16x2 -160 + -48x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -160 + -48x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-10 + -3x + x2) = 0 Factor a trinomial. 16((-2 + -1x)(5 + -1x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 5Solution
x = {-2, 5}
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