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Simplifying 18 = (2x + 5)(x + 7) Reorder the terms: 18 = (5 + 2x)(x + 7) Reorder the terms: 18 = (5 + 2x)(7 + x) Multiply (5 + 2x) * (7 + x) 18 = (5(7 + x) + 2x * (7 + x)) 18 = ((7 * 5 + x * 5) + 2x * (7 + x)) 18 = ((35 + 5x) + 2x * (7 + x)) 18 = (35 + 5x + (7 * 2x + x * 2x)) 18 = (35 + 5x + (14x + 2x2)) Combine like terms: 5x + 14x = 19x 18 = (35 + 19x + 2x2) Solving 18 = 35 + 19x + 2x2 Solving for variable 'x'. Combine like terms: 18 + -35 = -17 -17 + -19x + -2x2 = 35 + 19x + 2x2 + -35 + -19x + -2x2 Reorder the terms: -17 + -19x + -2x2 = 35 + -35 + 19x + -19x + 2x2 + -2x2 Combine like terms: 35 + -35 = 0 -17 + -19x + -2x2 = 0 + 19x + -19x + 2x2 + -2x2 -17 + -19x + -2x2 = 19x + -19x + 2x2 + -2x2 Combine like terms: 19x + -19x = 0 -17 + -19x + -2x2 = 0 + 2x2 + -2x2 -17 + -19x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -17 + -19x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 19x + 2x2) = 0 Factor a trinomial. -1((17 + 2x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 2x)' equal to zero and attempt to solve: Simplifying 17 + 2x = 0 Solving 17 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 2x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 2x = 0 + -17 2x = 0 + -17 Combine like terms: 0 + -17 = -17 2x = -17 Divide each side by '2'. x = -8.5 Simplifying x = -8.5Subproblem 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 = {-8.5, -1}
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