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Simplifying 9Q + 3Q2 = 210 Solving 9Q + 3Q2 = 210 Solving for variable 'Q'. Reorder the terms: -210 + 9Q + 3Q2 = 210 + -210 Combine like terms: 210 + -210 = 0 -210 + 9Q + 3Q2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-70 + 3Q + Q2) = 0 Factor a trinomial. 3((-10 + -1Q)(7 + -1Q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -1Q)' equal to zero and attempt to solve: Simplifying -10 + -1Q = 0 Solving -10 + -1Q = 0 Move all terms containing Q to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1Q = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1Q = 0 + 10 -1Q = 0 + 10 Combine like terms: 0 + 10 = 10 -1Q = 10 Divide each side by '-1'. Q = -10 Simplifying Q = -10Subproblem 2
Set the factor '(7 + -1Q)' equal to zero and attempt to solve: Simplifying 7 + -1Q = 0 Solving 7 + -1Q = 0 Move all terms containing Q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1Q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1Q = 0 + -7 -1Q = 0 + -7 Combine like terms: 0 + -7 = -7 -1Q = -7 Divide each side by '-1'. Q = 7 Simplifying Q = 7Solution
Q = {-10, 7}
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