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Simplifying 210x2 + -1680x + 7700 = 6230 Reorder the terms: 7700 + -1680x + 210x2 = 6230 Solving 7700 + -1680x + 210x2 = 6230 Solving for variable 'x'. Reorder the terms: 7700 + -6230 + -1680x + 210x2 = 6230 + -6230 Combine like terms: 7700 + -6230 = 1470 1470 + -1680x + 210x2 = 6230 + -6230 Combine like terms: 6230 + -6230 = 0 1470 + -1680x + 210x2 = 0 Factor out the Greatest Common Factor (GCF), '210'. 210(7 + -8x + x2) = 0 Factor a trinomial. 210((1 + -1x)(7 + -1x)) = 0 Ignore the factor 210.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1, 7}
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