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Simplifying 10q2 + -70q + -180 = 0 Reorder the terms: -180 + -70q + 10q2 = 0 Solving -180 + -70q + 10q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '10'. 10(-18 + -7q + q2) = 0 Factor a trinomial. 10((-2 + -1q)(9 + -1q)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-2 + -1q)' equal to zero and attempt to solve: Simplifying -2 + -1q = 0 Solving -2 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1q = 0 + 2 -1q = 0 + 2 Combine like terms: 0 + 2 = 2 -1q = 2 Divide each side by '-1'. q = -2 Simplifying q = -2Subproblem 2
Set the factor '(9 + -1q)' equal to zero and attempt to solve: Simplifying 9 + -1q = 0 Solving 9 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1q = 0 + -9 -1q = 0 + -9 Combine like terms: 0 + -9 = -9 -1q = -9 Divide each side by '-1'. q = 9 Simplifying q = 9Solution
q = {-2, 9}
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