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Simplifying 32x(x + 5) = 4800 Reorder the terms: 32x(5 + x) = 4800 (5 * 32x + x * 32x) = 4800 (160x + 32x2) = 4800 Solving 160x + 32x2 = 4800 Solving for variable 'x'. Reorder the terms: -4800 + 160x + 32x2 = 4800 + -4800 Combine like terms: 4800 + -4800 = 0 -4800 + 160x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '32'. 32(-150 + 5x + x2) = 0 Factor a trinomial. 32((-15 + -1x)(10 + -1x)) = 0 Ignore the factor 32.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 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 = {-15, 10}
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