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Simplifying 7q2 = 30 + -11q Solving 7q2 = 30 + -11q Solving for variable 'q'. Reorder the terms: -30 + 11q + 7q2 = 30 + -11q + -30 + 11q Reorder the terms: -30 + 11q + 7q2 = 30 + -30 + -11q + 11q Combine like terms: 30 + -30 = 0 -30 + 11q + 7q2 = 0 + -11q + 11q -30 + 11q + 7q2 = -11q + 11q Combine like terms: -11q + 11q = 0 -30 + 11q + 7q2 = 0 Factor a trinomial. (-3 + -1q)(10 + -7q) = 0Subproblem 1
Set the factor '(-3 + -1q)' equal to zero and attempt to solve: Simplifying -3 + -1q = 0 Solving -3 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1q = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1q = 0 + 3 -1q = 0 + 3 Combine like terms: 0 + 3 = 3 -1q = 3 Divide each side by '-1'. q = -3 Simplifying q = -3Subproblem 2
Set the factor '(10 + -7q)' equal to zero and attempt to solve: Simplifying 10 + -7q = 0 Solving 10 + -7q = 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 + -7q = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7q = 0 + -10 -7q = 0 + -10 Combine like terms: 0 + -10 = -10 -7q = -10 Divide each side by '-7'. q = 1.428571429 Simplifying q = 1.428571429Solution
q = {-3, 1.428571429}
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