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Simplifying 3q2 + -7 + q2 + q = 11 Reorder the terms: -7 + q + 3q2 + q2 = 11 Combine like terms: 3q2 + q2 = 4q2 -7 + q + 4q2 = 11 Solving -7 + q + 4q2 = 11 Solving for variable 'q'. Reorder the terms: -7 + -11 + q + 4q2 = 11 + -11 Combine like terms: -7 + -11 = -18 -18 + q + 4q2 = 11 + -11 Combine like terms: 11 + -11 = 0 -18 + q + 4q2 = 0 Factor a trinomial. (-9 + -4q)(2 + -1q) = 0Subproblem 1
Set the factor '(-9 + -4q)' equal to zero and attempt to solve: Simplifying -9 + -4q = 0 Solving -9 + -4q = 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 + -4q = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4q = 0 + 9 -4q = 0 + 9 Combine like terms: 0 + 9 = 9 -4q = 9 Divide each side by '-4'. q = -2.25 Simplifying q = -2.25Subproblem 2
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 = 2Solution
q = {-2.25, 2}
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