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Simplifying 0 = (x + 1)(2x + 7) Reorder the terms: 0 = (1 + x)(2x + 7) Reorder the terms: 0 = (1 + x)(7 + 2x) Multiply (1 + x) * (7 + 2x) 0 = (1(7 + 2x) + x(7 + 2x)) 0 = ((7 * 1 + 2x * 1) + x(7 + 2x)) 0 = ((7 + 2x) + x(7 + 2x)) 0 = (7 + 2x + (7 * x + 2x * x)) 0 = (7 + 2x + (7x + 2x2)) Combine like terms: 2x + 7x = 9x 0 = (7 + 9x + 2x2) Solving 0 = 7 + 9x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -9x + -2x2 = 7 + 9x + 2x2 + -7 + -9x + -2x2 Reorder the terms: -7 + -9x + -2x2 = 7 + -7 + 9x + -9x + 2x2 + -2x2 Combine like terms: 7 + -7 = 0 -7 + -9x + -2x2 = 0 + 9x + -9x + 2x2 + -2x2 -7 + -9x + -2x2 = 9x + -9x + 2x2 + -2x2 Combine like terms: 9x + -9x = 0 -7 + -9x + -2x2 = 0 + 2x2 + -2x2 -7 + -9x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -7 + -9x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 9x + 2x2) = 0 Factor a trinomial. -1((7 + 2x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 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 = {-3.5, -1}
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