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Simplifying (20 + 2x)(50 + 2x) = 0 Multiply (20 + 2x) * (50 + 2x) (20(50 + 2x) + 2x * (50 + 2x)) = 0 ((50 * 20 + 2x * 20) + 2x * (50 + 2x)) = 0 ((1000 + 40x) + 2x * (50 + 2x)) = 0 (1000 + 40x + (50 * 2x + 2x * 2x)) = 0 (1000 + 40x + (100x + 4x2)) = 0 Combine like terms: 40x + 100x = 140x (1000 + 140x + 4x2) = 0 Solving 1000 + 140x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(250 + 35x + x2) = 0 Factor a trinomial. 4((25 + x)(10 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + x)' equal to zero and attempt to solve: Simplifying 25 + x = 0 Solving 25 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + x = 0 + -25 x = 0 + -25 Combine like terms: 0 + -25 = -25 x = -25 Simplifying x = -25Subproblem 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 = {-25, -10}
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