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Simplifying 30b2 + -25bq + 18bq + -15q2 = 0 Reorder the terms: -25bq + 18bq + 30b2 + -15q2 = 0 Combine like terms: -25bq + 18bq = -7bq -7bq + 30b2 + -15q2 = 0 Solving -7bq + 30b2 + -15q2 = 0 Solving for variable 'b'. Factor a trinomial. (6b + -5q)(5b + 3q) = 0Subproblem 1
Set the factor '(6b + -5q)' equal to zero and attempt to solve: Simplifying 6b + -5q = 0 Solving 6b + -5q = 0 Move all terms containing b to the left, all other terms to the right. Add '5q' to each side of the equation. 6b + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 6b + 0 = 0 + 5q 6b = 0 + 5q Remove the zero: 6b = 5q Divide each side by '6'. b = 0.8333333333q Simplifying b = 0.8333333333qSubproblem 2
Set the factor '(5b + 3q)' equal to zero and attempt to solve: Simplifying 5b + 3q = 0 Solving 5b + 3q = 0 Move all terms containing b to the left, all other terms to the right. Add '-3q' to each side of the equation. 5b + 3q + -3q = 0 + -3q Combine like terms: 3q + -3q = 0 5b + 0 = 0 + -3q 5b = 0 + -3q Remove the zero: 5b = -3q Divide each side by '5'. b = -0.6q Simplifying b = -0.6qSolution
b = {0.8333333333q, -0.6q}
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