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Simplifying 210x2 + -1680x + 7700 = 17780 Reorder the terms: 7700 + -1680x + 210x2 = 17780 Solving 7700 + -1680x + 210x2 = 17780 Solving for variable 'x'. Reorder the terms: 7700 + -17780 + -1680x + 210x2 = 17780 + -17780 Combine like terms: 7700 + -17780 = -10080 -10080 + -1680x + 210x2 = 17780 + -17780 Combine like terms: 17780 + -17780 = 0 -10080 + -1680x + 210x2 = 0 Factor out the Greatest Common Factor (GCF), '210'. 210(-48 + -8x + x2) = 0 Factor a trinomial. 210((-4 + -1x)(12 + -1x)) = 0 Ignore the factor 210.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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {-4, 12}
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