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Simplifying x(x + -1) + -1(x + -5)(1) = 20 Reorder the terms: x(-1 + x) + -1(x + -5)(1) = 20 (-1 * x + x * x) + -1(x + -5)(1) = 20 (-1x + x2) + -1(x + -5)(1) = 20 Reorder the terms: -1x + x2 + -1(-5 + x)(1) = 20 Reorder the terms for easier multiplication: -1x + x2 + -1 * 1(-5 + x) = 20 Multiply -1 * 1 -1x + x2 + -1(-5 + x) = 20 -1x + x2 + (-5 * -1 + x * -1) = 20 -1x + x2 + (5 + -1x) = 20 Reorder the terms: 5 + -1x + -1x + x2 = 20 Combine like terms: -1x + -1x = -2x 5 + -2x + x2 = 20 Solving 5 + -2x + x2 = 20 Solving for variable 'x'. Reorder the terms: 5 + -20 + -2x + x2 = 20 + -20 Combine like terms: 5 + -20 = -15 -15 + -2x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -15 + -2x + x2 = 0 Factor a trinomial. (-3 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
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 = 5Solution
x = {-3, 5}
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