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Simplifying (x + 40)(2x + 38) = 0 Reorder the terms: (40 + x)(2x + 38) = 0 Reorder the terms: (40 + x)(38 + 2x) = 0 Multiply (40 + x) * (38 + 2x) (40(38 + 2x) + x(38 + 2x)) = 0 ((38 * 40 + 2x * 40) + x(38 + 2x)) = 0 ((1520 + 80x) + x(38 + 2x)) = 0 (1520 + 80x + (38 * x + 2x * x)) = 0 (1520 + 80x + (38x + 2x2)) = 0 Combine like terms: 80x + 38x = 118x (1520 + 118x + 2x2) = 0 Solving 1520 + 118x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(760 + 59x + x2) = 0 Factor a trinomial. 2((40 + x)(19 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + x)' equal to zero and attempt to solve: Simplifying 40 + x = 0 Solving 40 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + x = 0 + -40 x = 0 + -40 Combine like terms: 0 + -40 = -40 x = -40 Simplifying x = -40Subproblem 2
Set the factor '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Simplifying x = -19Solution
x = {-40, -19}
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