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Simplifying 126q2 + -57qb + -105b2 = 0 Reorder the terms: -57bq + -105b2 + 126q2 = 0 Solving -57bq + -105b2 + 126q2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-19bq + -35b2 + 42q2) = 0 Factor a trinomial. 3((-5b + -7q)(7b + -6q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5b + -7q)' equal to zero and attempt to solve: Simplifying -5b + -7q = 0 Solving -5b + -7q = 0 Move all terms containing b to the left, all other terms to the right. Add '7q' to each side of the equation. -5b + -7q + 7q = 0 + 7q Combine like terms: -7q + 7q = 0 -5b + 0 = 0 + 7q -5b = 0 + 7q Remove the zero: -5b = 7q Divide each side by '-5'. b = -1.4q Simplifying b = -1.4qSubproblem 2
Set the factor '(7b + -6q)' equal to zero and attempt to solve: Simplifying 7b + -6q = 0 Solving 7b + -6q = 0 Move all terms containing b to the left, all other terms to the right. Add '6q' to each side of the equation. 7b + -6q + 6q = 0 + 6q Combine like terms: -6q + 6q = 0 7b + 0 = 0 + 6q 7b = 0 + 6q Remove the zero: 7b = 6q Divide each side by '7'. b = 0.8571428571q Simplifying b = 0.8571428571qSolution
b = {-1.4q, 0.8571428571q}
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