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Simplifying 7x2 + 112x + -11 = 108 Reorder the terms: -11 + 112x + 7x2 = 108 Solving -11 + 112x + 7x2 = 108 Solving for variable 'x'. Reorder the terms: -11 + -108 + 112x + 7x2 = 108 + -108 Combine like terms: -11 + -108 = -119 -119 + 112x + 7x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -119 + 112x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-17 + 16x + x2) = 0 Factor a trinomial. 7((-17 + -1x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve: Simplifying -17 + -1x = 0 Solving -17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x = 0 + 17 -1x = 0 + 17 Combine like terms: 0 + 17 = 17 -1x = 17 Divide each side by '-1'. x = -17 Simplifying x = -17Subproblem 2
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 = 1Solution
x = {-17, 1}
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