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Simplifying (2x + 7)(2x + 9) = 35 Reorder the terms: (7 + 2x)(2x + 9) = 35 Reorder the terms: (7 + 2x)(9 + 2x) = 35 Multiply (7 + 2x) * (9 + 2x) (7(9 + 2x) + 2x * (9 + 2x)) = 35 ((9 * 7 + 2x * 7) + 2x * (9 + 2x)) = 35 ((63 + 14x) + 2x * (9 + 2x)) = 35 (63 + 14x + (9 * 2x + 2x * 2x)) = 35 (63 + 14x + (18x + 4x2)) = 35 Combine like terms: 14x + 18x = 32x (63 + 32x + 4x2) = 35 Solving 63 + 32x + 4x2 = 35 Solving for variable 'x'. Reorder the terms: 63 + -35 + 32x + 4x2 = 35 + -35 Combine like terms: 63 + -35 = 28 28 + 32x + 4x2 = 35 + -35 Combine like terms: 35 + -35 = 0 28 + 32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + 8x + x2) = 0 Factor a trinomial. 4((7 + x)(1 + x)) = 0 Ignore the factor 4.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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