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Simplifying 0 = -100x2 + 4800x + -50204 Reorder the terms: 0 = -50204 + 4800x + -100x2 Solving 0 = -50204 + 4800x + -100x2 Solving for variable 'x'. Combine like terms: 0 + 50204 = 50204 50204 + -4800x + 100x2 = -50204 + 4800x + -100x2 + 50204 + -4800x + 100x2 Reorder the terms: 50204 + -4800x + 100x2 = -50204 + 50204 + 4800x + -4800x + -100x2 + 100x2 Combine like terms: -50204 + 50204 = 0 50204 + -4800x + 100x2 = 0 + 4800x + -4800x + -100x2 + 100x2 50204 + -4800x + 100x2 = 4800x + -4800x + -100x2 + 100x2 Combine like terms: 4800x + -4800x = 0 50204 + -4800x + 100x2 = 0 + -100x2 + 100x2 50204 + -4800x + 100x2 = -100x2 + 100x2 Combine like terms: -100x2 + 100x2 = 0 50204 + -4800x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(12551 + -1200x + 25x2) = 0 Factor a trinomial. 4((77 + -5x)(163 + -5x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(77 + -5x)' equal to zero and attempt to solve: Simplifying 77 + -5x = 0 Solving 77 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-77' to each side of the equation. 77 + -77 + -5x = 0 + -77 Combine like terms: 77 + -77 = 0 0 + -5x = 0 + -77 -5x = 0 + -77 Combine like terms: 0 + -77 = -77 -5x = -77 Divide each side by '-5'. x = 15.4 Simplifying x = 15.4Subproblem 2
Set the factor '(163 + -5x)' equal to zero and attempt to solve: Simplifying 163 + -5x = 0 Solving 163 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-163' to each side of the equation. 163 + -163 + -5x = 0 + -163 Combine like terms: 163 + -163 = 0 0 + -5x = 0 + -163 -5x = 0 + -163 Combine like terms: 0 + -163 = -163 -5x = -163 Divide each side by '-5'. x = 32.6 Simplifying x = 32.6Solution
x = {15.4, 32.6}
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