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Simplifying (70 + 2x)(50 + 2x) * x = 0 Reorder the terms for easier multiplication: x(70 + 2x)(50 + 2x) = 0 Multiply (70 + 2x) * (50 + 2x) x(70(50 + 2x) + 2x * (50 + 2x)) = 0 x((50 * 70 + 2x * 70) + 2x * (50 + 2x)) = 0 x((3500 + 140x) + 2x * (50 + 2x)) = 0 x(3500 + 140x + (50 * 2x + 2x * 2x)) = 0 x(3500 + 140x + (100x + 4x2)) = 0 Combine like terms: 140x + 100x = 240x x(3500 + 240x + 4x2) = 0 (3500 * x + 240x * x + 4x2 * x) = 0 (3500x + 240x2 + 4x3) = 0 Solving 3500x + 240x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(875 + 60x + x2) = 0 Factor a trinomial. 4x((35 + x)(25 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(35 + x)' equal to zero and attempt to solve: Simplifying 35 + x = 0 Solving 35 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + x = 0 + -35 x = 0 + -35 Combine like terms: 0 + -35 = -35 x = -35 Simplifying x = -35Subproblem 3
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 = -25Solution
x = {0, -35, -25}
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