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Simplifying 7q2 + -168q + -175 = 0 Reorder the terms: -175 + -168q + 7q2 = 0 Solving -175 + -168q + 7q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '7'. 7(-25 + -24q + q2) = 0 Factor a trinomial. 7((-1 + -1q)(25 + -1q)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -1q)' equal to zero and attempt to solve: Simplifying -1 + -1q = 0 Solving -1 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1q = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1q = 0 + 1 -1q = 0 + 1 Combine like terms: 0 + 1 = 1 -1q = 1 Divide each side by '-1'. q = -1 Simplifying q = -1Subproblem 2
Set the factor '(25 + -1q)' equal to zero and attempt to solve: Simplifying 25 + -1q = 0 Solving 25 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1q = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1q = 0 + -25 -1q = 0 + -25 Combine like terms: 0 + -25 = -25 -1q = -25 Divide each side by '-1'. q = 25 Simplifying q = 25Solution
q = {-1, 25}
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