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Simplifying 2250 = (200 + -25x)(9 + 3x) Multiply (200 + -25x) * (9 + 3x) 2250 = (200(9 + 3x) + -25x * (9 + 3x)) 2250 = ((9 * 200 + 3x * 200) + -25x * (9 + 3x)) 2250 = ((1800 + 600x) + -25x * (9 + 3x)) 2250 = (1800 + 600x + (9 * -25x + 3x * -25x)) 2250 = (1800 + 600x + (-225x + -75x2)) Combine like terms: 600x + -225x = 375x 2250 = (1800 + 375x + -75x2) Solving 2250 = 1800 + 375x + -75x2 Solving for variable 'x'. Combine like terms: 2250 + -1800 = 450 450 + -375x + 75x2 = 1800 + 375x + -75x2 + -1800 + -375x + 75x2 Reorder the terms: 450 + -375x + 75x2 = 1800 + -1800 + 375x + -375x + -75x2 + 75x2 Combine like terms: 1800 + -1800 = 0 450 + -375x + 75x2 = 0 + 375x + -375x + -75x2 + 75x2 450 + -375x + 75x2 = 375x + -375x + -75x2 + 75x2 Combine like terms: 375x + -375x = 0 450 + -375x + 75x2 = 0 + -75x2 + 75x2 450 + -375x + 75x2 = -75x2 + 75x2 Combine like terms: -75x2 + 75x2 = 0 450 + -375x + 75x2 = 0 Factor out the Greatest Common Factor (GCF), '75'. 75(6 + -5x + x2) = 0 Factor a trinomial. 75((2 + -1x)(3 + -1x)) = 0 Ignore the factor 75.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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {2, 3}
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