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Simplifying 7250 = -10x2 + 475x + 3500 Reorder the terms: 7250 = 3500 + 475x + -10x2 Solving 7250 = 3500 + 475x + -10x2 Solving for variable 'x'. Combine like terms: 7250 + -3500 = 3750 3750 + -475x + 10x2 = 3500 + 475x + -10x2 + -3500 + -475x + 10x2 Reorder the terms: 3750 + -475x + 10x2 = 3500 + -3500 + 475x + -475x + -10x2 + 10x2 Combine like terms: 3500 + -3500 = 0 3750 + -475x + 10x2 = 0 + 475x + -475x + -10x2 + 10x2 3750 + -475x + 10x2 = 475x + -475x + -10x2 + 10x2 Combine like terms: 475x + -475x = 0 3750 + -475x + 10x2 = 0 + -10x2 + 10x2 3750 + -475x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 3750 + -475x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(750 + -95x + 2x2) = 0 Factor a trinomial. 5((10 + -1x)(75 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(75 + -2x)' equal to zero and attempt to solve: Simplifying 75 + -2x = 0 Solving 75 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + -2x = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -2x = 0 + -75 -2x = 0 + -75 Combine like terms: 0 + -75 = -75 -2x = -75 Divide each side by '-2'. x = 37.5 Simplifying x = 37.5Solution
x = {10, 37.5}
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