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Simplifying x(8x + 32) = 40 Reorder the terms: x(32 + 8x) = 40 (32 * x + 8x * x) = 40 (32x + 8x2) = 40 Solving 32x + 8x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + 32x + 8x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 32x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + 4x + x2) = 0 Factor a trinomial. 8((-5 + -1x)(1 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
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 = 1Solution
x = {-5, 1}
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