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Simplifying x(32 + -2x) = 128 (32 * x + -2x * x) = 128 (32x + -2x2) = 128 Solving 32x + -2x2 = 128 Solving for variable 'x'. Reorder the terms: -128 + 32x + -2x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -128 + 32x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + 16x + -1x2) = 0 Factor a trinomial. 2((-8 + x)(8 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {8, 8}
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