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Simplifying 7x2 + -7x + -17 = -3 Reorder the terms: -17 + -7x + 7x2 = -3 Solving -17 + -7x + 7x2 = -3 Solving for variable 'x'. Reorder the terms: -17 + 3 + -7x + 7x2 = -3 + 3 Combine like terms: -17 + 3 = -14 -14 + -7x + 7x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -14 + -7x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-2 + -1x + x2) = 0 Factor a trinomial. 7((-1 + -1x)(2 + -1x)) = 0 Ignore the factor 7.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-1, 2}
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