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Simplifying q2 + 30q = -4q2 + 10q + 25900 Reorder the terms: 30q + q2 = -4q2 + 10q + 25900 Reorder the terms: 30q + q2 = 25900 + 10q + -4q2 Solving 30q + q2 = 25900 + 10q + -4q2 Solving for variable 'q'. Reorder the terms: -25900 + 30q + -10q + q2 + 4q2 = 25900 + 10q + -4q2 + -25900 + -10q + 4q2 Combine like terms: 30q + -10q = 20q -25900 + 20q + q2 + 4q2 = 25900 + 10q + -4q2 + -25900 + -10q + 4q2 Combine like terms: q2 + 4q2 = 5q2 -25900 + 20q + 5q2 = 25900 + 10q + -4q2 + -25900 + -10q + 4q2 Reorder the terms: -25900 + 20q + 5q2 = 25900 + -25900 + 10q + -10q + -4q2 + 4q2 Combine like terms: 25900 + -25900 = 0 -25900 + 20q + 5q2 = 0 + 10q + -10q + -4q2 + 4q2 -25900 + 20q + 5q2 = 10q + -10q + -4q2 + 4q2 Combine like terms: 10q + -10q = 0 -25900 + 20q + 5q2 = 0 + -4q2 + 4q2 -25900 + 20q + 5q2 = -4q2 + 4q2 Combine like terms: -4q2 + 4q2 = 0 -25900 + 20q + 5q2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5180 + 4q + q2) = 0 Factor a trinomial. 5((-74 + -1q)(70 + -1q)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-74 + -1q)' equal to zero and attempt to solve: Simplifying -74 + -1q = 0 Solving -74 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '74' to each side of the equation. -74 + 74 + -1q = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -1q = 0 + 74 -1q = 0 + 74 Combine like terms: 0 + 74 = 74 -1q = 74 Divide each side by '-1'. q = -74 Simplifying q = -74Subproblem 2
Set the factor '(70 + -1q)' equal to zero and attempt to solve: Simplifying 70 + -1q = 0 Solving 70 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + -1q = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1q = 0 + -70 -1q = 0 + -70 Combine like terms: 0 + -70 = -70 -1q = -70 Divide each side by '-1'. q = 70 Simplifying q = 70Solution
q = {-74, 70}
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