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Simplifying (x + -7)(x + 7) = (x + 8)(x + 8) + -1 Reorder the terms: (-7 + x)(x + 7) = (x + 8)(x + 8) + -1 Reorder the terms: (-7 + x)(7 + x) = (x + 8)(x + 8) + -1 Multiply (-7 + x) * (7 + x) (-7(7 + x) + x(7 + x)) = (x + 8)(x + 8) + -1 ((7 * -7 + x * -7) + x(7 + x)) = (x + 8)(x + 8) + -1 ((-49 + -7x) + x(7 + x)) = (x + 8)(x + 8) + -1 (-49 + -7x + (7 * x + x * x)) = (x + 8)(x + 8) + -1 (-49 + -7x + (7x + x2)) = (x + 8)(x + 8) + -1 Combine like terms: -7x + 7x = 0 (-49 + 0 + x2) = (x + 8)(x + 8) + -1 (-49 + x2) = (x + 8)(x + 8) + -1 Reorder the terms: -49 + x2 = (8 + x)(x + 8) + -1 Reorder the terms: -49 + x2 = (8 + x)(8 + x) + -1 Multiply (8 + x) * (8 + x) -49 + x2 = (8(8 + x) + x(8 + x)) + -1 -49 + x2 = ((8 * 8 + x * 8) + x(8 + x)) + -1 -49 + x2 = ((64 + 8x) + x(8 + x)) + -1 -49 + x2 = (64 + 8x + (8 * x + x * x)) + -1 -49 + x2 = (64 + 8x + (8x + x2)) + -1 Combine like terms: 8x + 8x = 16x -49 + x2 = (64 + 16x + x2) + -1 Reorder the terms: -49 + x2 = 64 + -1 + 16x + x2 Combine like terms: 64 + -1 = 63 -49 + x2 = 63 + 16x + x2 Add '-1x2' to each side of the equation. -49 + x2 + -1x2 = 63 + 16x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -49 + 0 = 63 + 16x + x2 + -1x2 -49 = 63 + 16x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -49 = 63 + 16x + 0 -49 = 63 + 16x Solving -49 = 63 + 16x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16x' to each side of the equation. -49 + -16x = 63 + 16x + -16x Combine like terms: 16x + -16x = 0 -49 + -16x = 63 + 0 -49 + -16x = 63 Add '49' to each side of the equation. -49 + 49 + -16x = 63 + 49 Combine like terms: -49 + 49 = 0 0 + -16x = 63 + 49 -16x = 63 + 49 Combine like terms: 63 + 49 = 112 -16x = 112 Divide each side by '-16'. x = -7 Simplifying x = -7
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