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Simplifying (x + 5)(x + 1) = (x + 9)(x + -1) Reorder the terms: (5 + x)(x + 1) = (x + 9)(x + -1) Reorder the terms: (5 + x)(1 + x) = (x + 9)(x + -1) Multiply (5 + x) * (1 + x) (5(1 + x) + x(1 + x)) = (x + 9)(x + -1) ((1 * 5 + x * 5) + x(1 + x)) = (x + 9)(x + -1) ((5 + 5x) + x(1 + x)) = (x + 9)(x + -1) (5 + 5x + (1 * x + x * x)) = (x + 9)(x + -1) (5 + 5x + (1x + x2)) = (x + 9)(x + -1) Combine like terms: 5x + 1x = 6x (5 + 6x + x2) = (x + 9)(x + -1) Reorder the terms: 5 + 6x + x2 = (9 + x)(x + -1) Reorder the terms: 5 + 6x + x2 = (9 + x)(-1 + x) Multiply (9 + x) * (-1 + x) 5 + 6x + x2 = (9(-1 + x) + x(-1 + x)) 5 + 6x + x2 = ((-1 * 9 + x * 9) + x(-1 + x)) 5 + 6x + x2 = ((-9 + 9x) + x(-1 + x)) 5 + 6x + x2 = (-9 + 9x + (-1 * x + x * x)) 5 + 6x + x2 = (-9 + 9x + (-1x + x2)) Combine like terms: 9x + -1x = 8x 5 + 6x + x2 = (-9 + 8x + x2) Add '-1x2' to each side of the equation. 5 + 6x + x2 + -1x2 = -9 + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 6x + 0 = -9 + 8x + x2 + -1x2 5 + 6x = -9 + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 6x = -9 + 8x + 0 5 + 6x = -9 + 8x Solving 5 + 6x = -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. 5 + 6x + -8x = -9 + 8x + -8x Combine like terms: 6x + -8x = -2x 5 + -2x = -9 + 8x + -8x Combine like terms: 8x + -8x = 0 5 + -2x = -9 + 0 5 + -2x = -9 Add '-5' to each side of the equation. 5 + -5 + -2x = -9 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = -9 + -5 -2x = -9 + -5 Combine like terms: -9 + -5 = -14 -2x = -14 Divide each side by '-2'. x = 7 Simplifying x = 7
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