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Simplifying 19 = -3q2 + 29q + -49 Reorder the terms: 19 = -49 + 29q + -3q2 Solving 19 = -49 + 29q + -3q2 Solving for variable 'q'. Combine like terms: 19 + 49 = 68 68 + -29q + 3q2 = -49 + 29q + -3q2 + 49 + -29q + 3q2 Reorder the terms: 68 + -29q + 3q2 = -49 + 49 + 29q + -29q + -3q2 + 3q2 Combine like terms: -49 + 49 = 0 68 + -29q + 3q2 = 0 + 29q + -29q + -3q2 + 3q2 68 + -29q + 3q2 = 29q + -29q + -3q2 + 3q2 Combine like terms: 29q + -29q = 0 68 + -29q + 3q2 = 0 + -3q2 + 3q2 68 + -29q + 3q2 = -3q2 + 3q2 Combine like terms: -3q2 + 3q2 = 0 68 + -29q + 3q2 = 0 Factor a trinomial. (4 + -1q)(17 + -3q) = 0Subproblem 1
Set the factor '(4 + -1q)' equal to zero and attempt to solve: Simplifying 4 + -1q = 0 Solving 4 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1q = 0 + -4 -1q = 0 + -4 Combine like terms: 0 + -4 = -4 -1q = -4 Divide each side by '-1'. q = 4 Simplifying q = 4Subproblem 2
Set the factor '(17 + -3q)' equal to zero and attempt to solve: Simplifying 17 + -3q = 0 Solving 17 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -3q = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3q = 0 + -17 -3q = 0 + -17 Combine like terms: 0 + -17 = -17 -3q = -17 Divide each side by '-3'. q = 5.666666667 Simplifying q = 5.666666667Solution
q = {4, 5.666666667}
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