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Simplifying 4q2 + -4q = 3q2 + -6q + 35 Reorder the terms: -4q + 4q2 = 3q2 + -6q + 35 Reorder the terms: -4q + 4q2 = 35 + -6q + 3q2 Solving -4q + 4q2 = 35 + -6q + 3q2 Solving for variable 'q'. Reorder the terms: -35 + -4q + 6q + 4q2 + -3q2 = 35 + -6q + 3q2 + -35 + 6q + -3q2 Combine like terms: -4q + 6q = 2q -35 + 2q + 4q2 + -3q2 = 35 + -6q + 3q2 + -35 + 6q + -3q2 Combine like terms: 4q2 + -3q2 = 1q2 -35 + 2q + 1q2 = 35 + -6q + 3q2 + -35 + 6q + -3q2 Reorder the terms: -35 + 2q + 1q2 = 35 + -35 + -6q + 6q + 3q2 + -3q2 Combine like terms: 35 + -35 = 0 -35 + 2q + 1q2 = 0 + -6q + 6q + 3q2 + -3q2 -35 + 2q + 1q2 = -6q + 6q + 3q2 + -3q2 Combine like terms: -6q + 6q = 0 -35 + 2q + 1q2 = 0 + 3q2 + -3q2 -35 + 2q + 1q2 = 3q2 + -3q2 Combine like terms: 3q2 + -3q2 = 0 -35 + 2q + 1q2 = 0 Factor a trinomial. (-7 + -1q)(5 + -1q) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve: Simplifying 5 + -1q = 0 Solving 5 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1q = 0 + -5 -1q = 0 + -5 Combine like terms: 0 + -5 = -5 -1q = -5 Divide each side by '-1'. q = 5 Simplifying q = 5Solution
q = {-7, 5}
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