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Simplifying (4000 + -100X)(32 + X) = 129600 Multiply (4000 + -100X) * (32 + X) (4000(32 + X) + -100X * (32 + X)) = 129600 ((32 * 4000 + X * 4000) + -100X * (32 + X)) = 129600 ((128000 + 4000X) + -100X * (32 + X)) = 129600 (128000 + 4000X + (32 * -100X + X * -100X)) = 129600 (128000 + 4000X + (-3200X + -100X2)) = 129600 Combine like terms: 4000X + -3200X = 800X (128000 + 800X + -100X2) = 129600 Solving 128000 + 800X + -100X2 = 129600 Solving for variable 'X'. Reorder the terms: 128000 + -129600 + 800X + -100X2 = 129600 + -129600 Combine like terms: 128000 + -129600 = -1600 -1600 + 800X + -100X2 = 129600 + -129600 Combine like terms: 129600 + -129600 = 0 -1600 + 800X + -100X2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(-16 + 8X + -1X2) = 0 Factor a trinomial. 100((-4 + X)(4 + -1X)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-4 + X)' equal to zero and attempt to solve: Simplifying -4 + X = 0 Solving -4 + X = 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 + X = 0 + 4 Combine like terms: -4 + 4 = 0 0 + X = 0 + 4 X = 0 + 4 Combine like terms: 0 + 4 = 4 X = 4 Simplifying X = 4Subproblem 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 = {4, 4}
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