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Simplifying 12q2 + 34q + -28 = 0 Reorder the terms: -28 + 34q + 12q2 = 0 Solving -28 + 34q + 12q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 17q + 6q2) = 0 Factor a trinomial. 2((-7 + -2q)(2 + -3q)) = 0 Ignore the factor 2.Subproblem 1
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 = -3.5Subproblem 2
Set the factor '(2 + -3q)' equal to zero and attempt to solve: Simplifying 2 + -3q = 0 Solving 2 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3q = 0 + -2 -3q = 0 + -2 Combine like terms: 0 + -2 = -2 -3q = -2 Divide each side by '-3'. q = 0.6666666667 Simplifying q = 0.6666666667Solution
q = {-3.5, 0.6666666667}
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