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Simplifying 0 = -16x2 + 16x + 1440 Reorder the terms: 0 = 1440 + 16x + -16x2 Solving 0 = 1440 + 16x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -1440 = -1440 -1440 + -16x + 16x2 = 1440 + 16x + -16x2 + -1440 + -16x + 16x2 Reorder the terms: -1440 + -16x + 16x2 = 1440 + -1440 + 16x + -16x + -16x2 + 16x2 Combine like terms: 1440 + -1440 = 0 -1440 + -16x + 16x2 = 0 + 16x + -16x + -16x2 + 16x2 -1440 + -16x + 16x2 = 16x + -16x + -16x2 + 16x2 Combine like terms: 16x + -16x = 0 -1440 + -16x + 16x2 = 0 + -16x2 + 16x2 -1440 + -16x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -1440 + -16x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-90 + -1x + x2) = 0 Factor a trinomial. 16((-9 + -1x)(10 + -1x)) = 0 Ignore the factor 16.Subproblem 1
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 = -9Subproblem 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 = {-9, 10}
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