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Simplifying (x)(x + 2)(5) = 400 Reorder the terms: x(2 + x)(5) = 400 Reorder the terms for easier multiplication: 5x(2 + x) = 400 (2 * 5x + x * 5x) = 400 (10x + 5x2) = 400 Solving 10x + 5x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 10x + 5x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-80 + 2x + x2) = 0 Factor a trinomial. 5((-10 + -1x)(8 + -1x)) = 0 Ignore the factor 5.Subproblem 1
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 = -10Subproblem 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 = {-10, 8}
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