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Simplifying 8q2 + -24q = 14 Reorder the terms: -24q + 8q2 = 14 Solving -24q + 8q2 = 14 Solving for variable 'q'. Reorder the terms: -14 + -24q + 8q2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -24q + 8q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -12q + 4q2) = 0 Factor a trinomial. 2((-1 + -2q)(7 + -2q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2q)' equal to zero and attempt to solve: Simplifying -1 + -2q = 0 Solving -1 + -2q = 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 + -2q = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2q = 0 + 1 -2q = 0 + 1 Combine like terms: 0 + 1 = 1 -2q = 1 Divide each side by '-2'. q = -0.5 Simplifying q = -0.5Subproblem 2
Set the factor '(7 + -2q)' equal to zero and attempt to solve: Simplifying 7 + -2q = 0 Solving 7 + -2q = 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 + -2q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2q = 0 + -7 -2q = 0 + -7 Combine like terms: 0 + -7 = -7 -2q = -7 Divide each side by '-2'. q = 3.5 Simplifying q = 3.5Solution
q = {-0.5, 3.5}
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