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Simplifying 3q2 + -5q = 8 Reorder the terms: -5q + 3q2 = 8 Solving -5q + 3q2 = 8 Solving for variable 'q'. Reorder the terms: -8 + -5q + 3q2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -5q + 3q2 = 0 Factor a trinomial. (-1 + -1q)(8 + -3q) = 0Subproblem 1
Set the factor '(-1 + -1q)' equal to zero and attempt to solve: Simplifying -1 + -1q = 0 Solving -1 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1q = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1q = 0 + 1 -1q = 0 + 1 Combine like terms: 0 + 1 = 1 -1q = 1 Divide each side by '-1'. q = -1 Simplifying q = -1Subproblem 2
Set the factor '(8 + -3q)' equal to zero and attempt to solve: Simplifying 8 + -3q = 0 Solving 8 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3q = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3q = 0 + -8 -3q = 0 + -8 Combine like terms: 0 + -8 = -8 -3q = -8 Divide each side by '-3'. q = 2.666666667 Simplifying q = 2.666666667Solution
q = {-1, 2.666666667}
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