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Simplifying -4x2 + 150x = 1250 Reorder the terms: 150x + -4x2 = 1250 Solving 150x + -4x2 = 1250 Solving for variable 'x'. Reorder the terms: -1250 + 150x + -4x2 = 1250 + -1250 Combine like terms: 1250 + -1250 = 0 -1250 + 150x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-625 + 75x + -2x2) = 0 Factor a trinomial. 2((-25 + x)(25 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + x)' equal to zero and attempt to solve: Simplifying -25 + x = 0 Solving -25 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + x = 0 + 25 x = 0 + 25 Combine like terms: 0 + 25 = 25 x = 25 Simplifying x = 25Subproblem 2
Set the factor '(25 + -2x)' equal to zero and attempt to solve: Simplifying 25 + -2x = 0 Solving 25 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -2x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -2x = 0 + -25 -2x = 0 + -25 Combine like terms: 0 + -25 = -25 -2x = -25 Divide each side by '-2'. x = 12.5 Simplifying x = 12.5Solution
x = {25, 12.5}
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