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Simplifying 3000 = (200 + 8x)(15 + -0.50x) Multiply (200 + 8x) * (15 + -0.50x) 3000 = (200(15 + -0.50x) + 8x * (15 + -0.50x)) 3000 = ((15 * 200 + -0.50x * 200) + 8x * (15 + -0.50x)) 3000 = ((3000 + -100x) + 8x * (15 + -0.50x)) 3000 = (3000 + -100x + (15 * 8x + -0.50x * 8x)) 3000 = (3000 + -100x + (120x + -4x2)) Combine like terms: -100x + 120x = 20x 3000 = (3000 + 20x + -4x2) Add '-3000' to each side of the equation. 3000 + -3000 = 3000 + 20x + -3000 + -4x2 Combine like terms: 3000 + -3000 = 0 0 = 3000 + 20x + -3000 + -4x2 Reorder the terms: 0 = 3000 + -3000 + 20x + -4x2 Combine like terms: 3000 + -3000 = 0 0 = 0 + 20x + -4x2 0 = 20x + -4x2 Solving 0 = 20x + -4x2 Solving for variable 'x'. Remove the zero: -20x + 4x2 = 20x + -4x2 + -20x + 4x2 Reorder the terms: -20x + 4x2 = 20x + -20x + -4x2 + 4x2 Combine like terms: 20x + -20x = 0 -20x + 4x2 = 0 + -4x2 + 4x2 -20x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -20x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-5 + 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Solution
x = {0, 5}
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