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Simplifying 17600 = (90 + 5x)(200 + -10x) Multiply (90 + 5x) * (200 + -10x) 17600 = (90(200 + -10x) + 5x * (200 + -10x)) 17600 = ((200 * 90 + -10x * 90) + 5x * (200 + -10x)) 17600 = ((18000 + -900x) + 5x * (200 + -10x)) 17600 = (18000 + -900x + (200 * 5x + -10x * 5x)) 17600 = (18000 + -900x + (1000x + -50x2)) Combine like terms: -900x + 1000x = 100x 17600 = (18000 + 100x + -50x2) Solving 17600 = 18000 + 100x + -50x2 Solving for variable 'x'. Combine like terms: 17600 + -18000 = -400 -400 + -100x + 50x2 = 18000 + 100x + -50x2 + -18000 + -100x + 50x2 Reorder the terms: -400 + -100x + 50x2 = 18000 + -18000 + 100x + -100x + -50x2 + 50x2 Combine like terms: 18000 + -18000 = 0 -400 + -100x + 50x2 = 0 + 100x + -100x + -50x2 + 50x2 -400 + -100x + 50x2 = 100x + -100x + -50x2 + 50x2 Combine like terms: 100x + -100x = 0 -400 + -100x + 50x2 = 0 + -50x2 + 50x2 -400 + -100x + 50x2 = -50x2 + 50x2 Combine like terms: -50x2 + 50x2 = 0 -400 + -100x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-8 + -2x + x2) = 0 Factor a trinomial. 50((-2 + -1x)(4 + -1x)) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-2, 4}
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