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Simplifying 0 = -16x2 + 144x + 160 Reorder the terms: 0 = 160 + 144x + -16x2 Solving 0 = 160 + 144x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -160 = -160 -160 + -144x + 16x2 = 160 + 144x + -16x2 + -160 + -144x + 16x2 Reorder the terms: -160 + -144x + 16x2 = 160 + -160 + 144x + -144x + -16x2 + 16x2 Combine like terms: 160 + -160 = 0 -160 + -144x + 16x2 = 0 + 144x + -144x + -16x2 + 16x2 -160 + -144x + 16x2 = 144x + -144x + -16x2 + 16x2 Combine like terms: 144x + -144x = 0 -160 + -144x + 16x2 = 0 + -16x2 + 16x2 -160 + -144x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -160 + -144x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-10 + -9x + x2) = 0 Factor a trinomial. 16((-1 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-1, 10}
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