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Simplifying 2(x + 1)(x + 7) = 14 Reorder the terms: 2(1 + x)(x + 7) = 14 Reorder the terms: 2(1 + x)(7 + x) = 14 Multiply (1 + x) * (7 + x) 2(1(7 + x) + x(7 + x)) = 14 2((7 * 1 + x * 1) + x(7 + x)) = 14 2((7 + 1x) + x(7 + x)) = 14 2(7 + 1x + (7 * x + x * x)) = 14 2(7 + 1x + (7x + x2)) = 14 Combine like terms: 1x + 7x = 8x 2(7 + 8x + x2) = 14 (7 * 2 + 8x * 2 + x2 * 2) = 14 (14 + 16x + 2x2) = 14 Add '-14' to each side of the equation. 14 + 16x + -14 + 2x2 = 14 + -14 Reorder the terms: 14 + -14 + 16x + 2x2 = 14 + -14 Combine like terms: 14 + -14 = 0 0 + 16x + 2x2 = 14 + -14 16x + 2x2 = 14 + -14 Combine like terms: 14 + -14 = 0 16x + 2x2 = 0 Solving 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(8 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {0, -8}
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