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Simplifying 140 = -16x2 + 22x + 160 Reorder the terms: 140 = 160 + 22x + -16x2 Solving 140 = 160 + 22x + -16x2 Solving for variable 'x'. Combine like terms: 140 + -160 = -20 -20 + -22x + 16x2 = 160 + 22x + -16x2 + -160 + -22x + 16x2 Reorder the terms: -20 + -22x + 16x2 = 160 + -160 + 22x + -22x + -16x2 + 16x2 Combine like terms: 160 + -160 = 0 -20 + -22x + 16x2 = 0 + 22x + -22x + -16x2 + 16x2 -20 + -22x + 16x2 = 22x + -22x + -16x2 + 16x2 Combine like terms: 22x + -22x = 0 -20 + -22x + 16x2 = 0 + -16x2 + 16x2 -20 + -22x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -20 + -22x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -11x + 8x2) = 0 Factor a trinomial. 2((-5 + -8x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -8x)' equal to zero and attempt to solve: Simplifying -5 + -8x = 0 Solving -5 + -8x = 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 + -8x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8x = 0 + 5 -8x = 0 + 5 Combine like terms: 0 + 5 = 5 -8x = 5 Divide each side by '-8'. x = -0.625 Simplifying x = -0.625Subproblem 2
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 = 2Solution
x = {-0.625, 2}
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