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Simplifying 5000 = -30x2 + 520x + 3400 Reorder the terms: 5000 = 3400 + 520x + -30x2 Solving 5000 = 3400 + 520x + -30x2 Solving for variable 'x'. Combine like terms: 5000 + -3400 = 1600 1600 + -520x + 30x2 = 3400 + 520x + -30x2 + -3400 + -520x + 30x2 Reorder the terms: 1600 + -520x + 30x2 = 3400 + -3400 + 520x + -520x + -30x2 + 30x2 Combine like terms: 3400 + -3400 = 0 1600 + -520x + 30x2 = 0 + 520x + -520x + -30x2 + 30x2 1600 + -520x + 30x2 = 520x + -520x + -30x2 + 30x2 Combine like terms: 520x + -520x = 0 1600 + -520x + 30x2 = 0 + -30x2 + 30x2 1600 + -520x + 30x2 = -30x2 + 30x2 Combine like terms: -30x2 + 30x2 = 0 1600 + -520x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(160 + -52x + 3x2) = 0 Factor a trinomial. 10((4 + -1x)(40 + -3x)) = 0 Ignore the factor 10.Subproblem 1
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 = 4Subproblem 2
Set the factor '(40 + -3x)' equal to zero and attempt to solve: Simplifying 40 + -3x = 0 Solving 40 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -3x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -3x = 0 + -40 -3x = 0 + -40 Combine like terms: 0 + -40 = -40 -3x = -40 Divide each side by '-3'. x = 13.33333333 Simplifying x = 13.33333333Solution
x = {4, 13.33333333}
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