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Simplifying 0 = 100x2 + 1900x + -299000 Reorder the terms: 0 = -299000 + 1900x + 100x2 Solving 0 = -299000 + 1900x + 100x2 Solving for variable 'x'. Combine like terms: 0 + 299000 = 299000 299000 + -1900x + -100x2 = -299000 + 1900x + 100x2 + 299000 + -1900x + -100x2 Reorder the terms: 299000 + -1900x + -100x2 = -299000 + 299000 + 1900x + -1900x + 100x2 + -100x2 Combine like terms: -299000 + 299000 = 0 299000 + -1900x + -100x2 = 0 + 1900x + -1900x + 100x2 + -100x2 299000 + -1900x + -100x2 = 1900x + -1900x + 100x2 + -100x2 Combine like terms: 1900x + -1900x = 0 299000 + -1900x + -100x2 = 0 + 100x2 + -100x2 299000 + -1900x + -100x2 = 100x2 + -100x2 Combine like terms: 100x2 + -100x2 = 0 299000 + -1900x + -100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(2990 + -19x + -1x2) = 0 Factor a trinomial. 100((46 + -1x)(65 + x)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(46 + -1x)' equal to zero and attempt to solve: Simplifying 46 + -1x = 0 Solving 46 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + -1x = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -1x = 0 + -46 -1x = 0 + -46 Combine like terms: 0 + -46 = -46 -1x = -46 Divide each side by '-1'. x = 46 Simplifying x = 46Subproblem 2
Set the factor '(65 + x)' equal to zero and attempt to solve: Simplifying 65 + x = 0 Solving 65 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + -65 + x = 0 + -65 Combine like terms: 65 + -65 = 0 0 + x = 0 + -65 x = 0 + -65 Combine like terms: 0 + -65 = -65 x = -65 Simplifying x = -65Solution
x = {46, -65}
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