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Simplifying 2X(38 + 32 + -2X) = 600 Combine like terms: 38 + 32 = 70 2X(70 + -2X) = 600 (70 * 2X + -2X * 2X) = 600 (140X + -4X2) = 600 Solving 140X + -4X2 = 600 Solving for variable 'X'. Reorder the terms: -600 + 140X + -4X2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 140X + -4X2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-150 + 35X + -1X2) = 0 Factor a trinomial. 4((-30 + X)(5 + -1X)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-30 + X)' equal to zero and attempt to solve: Simplifying -30 + X = 0 Solving -30 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + X = 0 + 30 Combine like terms: -30 + 30 = 0 0 + X = 0 + 30 X = 0 + 30 Combine like terms: 0 + 30 = 30 X = 30 Simplifying X = 30Subproblem 2
Set the factor '(5 + -1X)' equal to zero and attempt to solve: Simplifying 5 + -1X = 0 Solving 5 + -1X = 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 + -1X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1X = 0 + -5 -1X = 0 + -5 Combine like terms: 0 + -5 = -5 -1X = -5 Divide each side by '-1'. X = 5 Simplifying X = 5Solution
X = {30, 5}
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