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Simplifying x(x + -1) = (x + -5)(2x + 7) Reorder the terms: x(-1 + x) = (x + -5)(2x + 7) (-1 * x + x * x) = (x + -5)(2x + 7) (-1x + x2) = (x + -5)(2x + 7) Reorder the terms: -1x + x2 = (-5 + x)(2x + 7) Reorder the terms: -1x + x2 = (-5 + x)(7 + 2x) Multiply (-5 + x) * (7 + 2x) -1x + x2 = (-5(7 + 2x) + x(7 + 2x)) -1x + x2 = ((7 * -5 + 2x * -5) + x(7 + 2x)) -1x + x2 = ((-35 + -10x) + x(7 + 2x)) -1x + x2 = (-35 + -10x + (7 * x + 2x * x)) -1x + x2 = (-35 + -10x + (7x + 2x2)) Combine like terms: -10x + 7x = -3x -1x + x2 = (-35 + -3x + 2x2) Solving -1x + x2 = -35 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: 35 + -1x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2 Combine like terms: -1x + 3x = 2x 35 + 2x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2 Combine like terms: x2 + -2x2 = -1x2 35 + 2x + -1x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2 Reorder the terms: 35 + 2x + -1x2 = -35 + 35 + -3x + 3x + 2x2 + -2x2 Combine like terms: -35 + 35 = 0 35 + 2x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2 35 + 2x + -1x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 35 + 2x + -1x2 = 0 + 2x2 + -2x2 35 + 2x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 35 + 2x + -1x2 = 0 Factor a trinomial. (7 + -1x)(5 + x) = 0Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {7, -5}
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