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Simplifying (5x + 5)(2x + 7) = 0 Reorder the terms: (5 + 5x)(2x + 7) = 0 Reorder the terms: (5 + 5x)(7 + 2x) = 0 Multiply (5 + 5x) * (7 + 2x) (5(7 + 2x) + 5x * (7 + 2x)) = 0 ((7 * 5 + 2x * 5) + 5x * (7 + 2x)) = 0 ((35 + 10x) + 5x * (7 + 2x)) = 0 (35 + 10x + (7 * 5x + 2x * 5x)) = 0 (35 + 10x + (35x + 10x2)) = 0 Combine like terms: 10x + 35x = 45x (35 + 45x + 10x2) = 0 Solving 35 + 45x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(7 + 9x + 2x2) = 0 Factor a trinomial. 5((7 + 2x)(1 + x)) = 0 Ignore the factor 5.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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