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Simplifying 12135 = x2 + -10x + 60 Reorder the terms: 12135 = 60 + -10x + x2 Solving 12135 = 60 + -10x + x2 Solving for variable 'x'. Combine like terms: 12135 + -60 = 12075 12075 + 10x + -1x2 = 60 + -10x + x2 + -60 + 10x + -1x2 Reorder the terms: 12075 + 10x + -1x2 = 60 + -60 + -10x + 10x + x2 + -1x2 Combine like terms: 60 + -60 = 0 12075 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2 12075 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 12075 + 10x + -1x2 = 0 + x2 + -1x2 12075 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12075 + 10x + -1x2 = 0 Factor a trinomial. (115 + -1x)(105 + x) = 0Subproblem 1
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 = 115Subproblem 2
Set the factor '(105 + x)' equal to zero and attempt to solve: Simplifying 105 + x = 0 Solving 105 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-105' to each side of the equation. 105 + -105 + x = 0 + -105 Combine like terms: 105 + -105 = 0 0 + x = 0 + -105 x = 0 + -105 Combine like terms: 0 + -105 = -105 x = -105 Simplifying x = -105Solution
x = {115, -105}
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