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Simplifying 0 = -16x2 + 24x + 160 Reorder the terms: 0 = 160 + 24x + -16x2 Solving 0 = 160 + 24x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -160 = -160 -160 + -24x + 16x2 = 160 + 24x + -16x2 + -160 + -24x + 16x2 Reorder the terms: -160 + -24x + 16x2 = 160 + -160 + 24x + -24x + -16x2 + 16x2 Combine like terms: 160 + -160 = 0 -160 + -24x + 16x2 = 0 + 24x + -24x + -16x2 + 16x2 -160 + -24x + 16x2 = 24x + -24x + -16x2 + 16x2 Combine like terms: 24x + -24x = 0 -160 + -24x + 16x2 = 0 + -16x2 + 16x2 -160 + -24x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -160 + -24x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-20 + -3x + 2x2) = 0 Factor a trinomial. 8((-5 + -2x)(4 + -1x)) = 0 Ignore the factor 8.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 '(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 = 4Solution
x = {-2.5, 4}
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