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Simplifying x(x + -5) = (x + -1)(x + -1) + -13 Reorder the terms: x(-5 + x) = (x + -1)(x + -1) + -13 (-5 * x + x * x) = (x + -1)(x + -1) + -13 (-5x + x2) = (x + -1)(x + -1) + -13 Reorder the terms: -5x + x2 = (-1 + x)(x + -1) + -13 Reorder the terms: -5x + x2 = (-1 + x)(-1 + x) + -13 Multiply (-1 + x) * (-1 + x) -5x + x2 = (-1(-1 + x) + x(-1 + x)) + -13 -5x + x2 = ((-1 * -1 + x * -1) + x(-1 + x)) + -13 -5x + x2 = ((1 + -1x) + x(-1 + x)) + -13 -5x + x2 = (1 + -1x + (-1 * x + x * x)) + -13 -5x + x2 = (1 + -1x + (-1x + x2)) + -13 Combine like terms: -1x + -1x = -2x -5x + x2 = (1 + -2x + x2) + -13 Reorder the terms: -5x + x2 = 1 + -13 + -2x + x2 Combine like terms: 1 + -13 = -12 -5x + x2 = -12 + -2x + x2 Add '-1x2' to each side of the equation. -5x + x2 + -1x2 = -12 + -2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -5x + 0 = -12 + -2x + x2 + -1x2 -5x = -12 + -2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -5x = -12 + -2x + 0 -5x = -12 + -2x Solving -5x = -12 + -2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2x' to each side of the equation. -5x + 2x = -12 + -2x + 2x Combine like terms: -5x + 2x = -3x -3x = -12 + -2x + 2x Combine like terms: -2x + 2x = 0 -3x = -12 + 0 -3x = -12 Divide each side by '-3'. x = 4 Simplifying x = 4
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