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Simplifying -0.5 * 32x2 + 2000x + 0 = 40000 Multiply -0.5 * 32 -16x2 + 2000x + 0 = 40000 Reorder the terms: 0 + 2000x + -16x2 = 40000 Remove the zero: 2000x + -16x2 = 40000 Solving 2000x + -16x2 = 40000 Solving for variable 'x'. Reorder the terms: -40000 + 2000x + -16x2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -40000 + 2000x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-2500 + 125x + -1x2) = 0 Factor a trinomial. 16((-100 + x)(25 + -1x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-100 + x)' equal to zero and attempt to solve: Simplifying -100 + x = 0 Solving -100 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 0 + 100 Combine like terms: -100 + 100 = 0 0 + x = 0 + 100 x = 0 + 100 Combine like terms: 0 + 100 = 100 x = 100 Simplifying x = 100Subproblem 2
Set the factor '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 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 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Divide each side by '-1'. x = 25 Simplifying x = 25Solution
x = {100, 25}
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