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Simplifying x(x + 5) = (x + 9)(x + -1) Reorder the terms: x(5 + x) = (x + 9)(x + -1) (5 * x + x * x) = (x + 9)(x + -1) (5x + x2) = (x + 9)(x + -1) Reorder the terms: 5x + x2 = (9 + x)(x + -1) Reorder the terms: 5x + x2 = (9 + x)(-1 + x) Multiply (9 + x) * (-1 + x) 5x + x2 = (9(-1 + x) + x(-1 + x)) 5x + x2 = ((-1 * 9 + x * 9) + x(-1 + x)) 5x + x2 = ((-9 + 9x) + x(-1 + x)) 5x + x2 = (-9 + 9x + (-1 * x + x * x)) 5x + x2 = (-9 + 9x + (-1x + x2)) Combine like terms: 9x + -1x = 8x 5x + x2 = (-9 + 8x + x2) Add '-1x2' to each side of the equation. 5x + x2 + -1x2 = -9 + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5x + 0 = -9 + 8x + x2 + -1x2 5x = -9 + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5x = -9 + 8x + 0 5x = -9 + 8x Solving 5x = -9 + 8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. 5x + -8x = -9 + 8x + -8x Combine like terms: 5x + -8x = -3x -3x = -9 + 8x + -8x Combine like terms: 8x + -8x = 0 -3x = -9 + 0 -3x = -9 Divide each side by '-3'. x = 3 Simplifying x = 3
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