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Simplifying (40 + 2x)(20 + 2x) = 0 Multiply (40 + 2x) * (20 + 2x) (40(20 + 2x) + 2x * (20 + 2x)) = 0 ((20 * 40 + 2x * 40) + 2x * (20 + 2x)) = 0 ((800 + 80x) + 2x * (20 + 2x)) = 0 (800 + 80x + (20 * 2x + 2x * 2x)) = 0 (800 + 80x + (40x + 4x2)) = 0 Combine like terms: 80x + 40x = 120x (800 + 120x + 4x2) = 0 Solving 800 + 120x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(200 + 30x + x2) = 0 Factor a trinomial. 4((20 + x)(10 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {-20, -10}
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