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Simplifying 2q2 + 10qb + 8b2 = 0 Reorder the terms: 10bq + 8b2 + 2q2 = 0 Solving 10bq + 8b2 + 2q2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(5bq + 4b2 + q2) = 0 Factor a trinomial. 2((4b + q)(b + q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4b + q)' equal to zero and attempt to solve: Simplifying 4b + q = 0 Solving 4b + q = 0 Move all terms containing b to the left, all other terms to the right. Add '-1q' to each side of the equation. 4b + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 4b + 0 = 0 + -1q 4b = 0 + -1q Remove the zero: 4b = -1q Divide each side by '4'. b = -0.25q Simplifying b = -0.25qSubproblem 2
Set the factor '(b + q)' equal to zero and attempt to solve: Simplifying b + q = 0 Solving b + q = 0 Move all terms containing b to the left, all other terms to the right. Add '-1q' to each side of the equation. b + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 b + 0 = 0 + -1q b = 0 + -1q Remove the zero: b = -1q Simplifying b = -1qSolution
b = {-0.25q, -1q}
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