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Simplifying 500x4 = -1000x3 + 24000x2 Reorder the terms: 500x4 = 24000x2 + -1000x3 Solving 500x4 = 24000x2 + -1000x3 Solving for variable 'x'. Reorder the terms: -24000x2 + 1000x3 + 500x4 = 24000x2 + -1000x3 + -24000x2 + 1000x3 Reorder the terms: -24000x2 + 1000x3 + 500x4 = 24000x2 + -24000x2 + -1000x3 + 1000x3 Combine like terms: 24000x2 + -24000x2 = 0 -24000x2 + 1000x3 + 500x4 = 0 + -1000x3 + 1000x3 -24000x2 + 1000x3 + 500x4 = -1000x3 + 1000x3 Combine like terms: -1000x3 + 1000x3 = 0 -24000x2 + 1000x3 + 500x4 = 0 Factor out the Greatest Common Factor (GCF), '500x2'. 500x2(-48 + 2x + x2) = 0 Factor a trinomial. 500x2((-8 + -1x)(6 + -1x)) = 0 Ignore the factor 500.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, -8, 6}
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