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Simplifying 15000 + -500x + 4x2 = 10400 Solving 15000 + -500x + 4x2 = 10400 Solving for variable 'x'. Reorder the terms: 15000 + -10400 + -500x + 4x2 = 10400 + -10400 Combine like terms: 15000 + -10400 = 4600 4600 + -500x + 4x2 = 10400 + -10400 Combine like terms: 10400 + -10400 = 0 4600 + -500x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1150 + -125x + x2) = 0 Factor a trinomial. 4((10 + -1x)(115 + -1x)) = 0 Ignore the factor 4.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 '(115 + -1x)' equal to zero and attempt to solve: Simplifying 115 + -1x = 0 Solving 115 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-115' to each side of the equation. 115 + -115 + -1x = 0 + -115 Combine like terms: 115 + -115 = 0 0 + -1x = 0 + -115 -1x = 0 + -115 Combine like terms: 0 + -115 = -115 -1x = -115 Divide each side by '-1'. x = 115 Simplifying x = 115Solution
x = {10, 115}
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