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Simplifying 0 = -16x2 + 128x + 144 Reorder the terms: 0 = 144 + 128x + -16x2 Solving 0 = 144 + 128x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -144 = -144 -144 + -128x + 16x2 = 144 + 128x + -16x2 + -144 + -128x + 16x2 Reorder the terms: -144 + -128x + 16x2 = 144 + -144 + 128x + -128x + -16x2 + 16x2 Combine like terms: 144 + -144 = 0 -144 + -128x + 16x2 = 0 + 128x + -128x + -16x2 + 16x2 -144 + -128x + 16x2 = 128x + -128x + -16x2 + 16x2 Combine like terms: 128x + -128x = 0 -144 + -128x + 16x2 = 0 + -16x2 + 16x2 -144 + -128x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -144 + -128x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-9 + -8x + x2) = 0 Factor a trinomial. 16((-1 + -1x)(9 + -1x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-1, 9}
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