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Simplifying x = (x + 7)(x + 7) + 8(x + 7) + -7 Reorder the terms: x = (7 + x)(x + 7) + 8(x + 7) + -7 Reorder the terms: x = (7 + x)(7 + x) + 8(x + 7) + -7 Multiply (7 + x) * (7 + x) x = (7(7 + x) + x(7 + x)) + 8(x + 7) + -7 x = ((7 * 7 + x * 7) + x(7 + x)) + 8(x + 7) + -7 x = ((49 + 7x) + x(7 + x)) + 8(x + 7) + -7 x = (49 + 7x + (7 * x + x * x)) + 8(x + 7) + -7 x = (49 + 7x + (7x + x2)) + 8(x + 7) + -7 Combine like terms: 7x + 7x = 14x x = (49 + 14x + x2) + 8(x + 7) + -7 Reorder the terms: x = 49 + 14x + x2 + 8(7 + x) + -7 x = 49 + 14x + x2 + (7 * 8 + x * 8) + -7 x = 49 + 14x + x2 + (56 + 8x) + -7 Reorder the terms: x = 49 + 56 + -7 + 14x + 8x + x2 Combine like terms: 49 + 56 = 105 x = 105 + -7 + 14x + 8x + x2 Combine like terms: 105 + -7 = 98 x = 98 + 14x + 8x + x2 Combine like terms: 14x + 8x = 22x x = 98 + 22x + x2 Solving x = 98 + 22x + x2 Solving for variable 'x'. Reorder the terms: -98 + x + -22x + -1x2 = 98 + 22x + x2 + -98 + -22x + -1x2 Combine like terms: x + -22x = -21x -98 + -21x + -1x2 = 98 + 22x + x2 + -98 + -22x + -1x2 Reorder the terms: -98 + -21x + -1x2 = 98 + -98 + 22x + -22x + x2 + -1x2 Combine like terms: 98 + -98 = 0 -98 + -21x + -1x2 = 0 + 22x + -22x + x2 + -1x2 -98 + -21x + -1x2 = 22x + -22x + x2 + -1x2 Combine like terms: 22x + -22x = 0 -98 + -21x + -1x2 = 0 + x2 + -1x2 -98 + -21x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -98 + -21x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(98 + 21x + x2) = 0 Factor a trinomial. -1((14 + x)(7 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {-14, -7}
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