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