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Simplifying 84q2 + -38qd + -70d2 = 0 Reorder the terms: -38dq + -70d2 + 84q2 = 0 Solving -38dq + -70d2 + 84q2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19dq + -35d2 + 42q2) = 0 Factor a trinomial. 2((-5d + -7q)(7d + -6q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5d + -7q)' equal to zero and attempt to solve: Simplifying -5d + -7q = 0 Solving -5d + -7q = 0 Move all terms containing d to the left, all other terms to the right. Add '7q' to each side of the equation. -5d + -7q + 7q = 0 + 7q Combine like terms: -7q + 7q = 0 -5d + 0 = 0 + 7q -5d = 0 + 7q Remove the zero: -5d = 7q Divide each side by '-5'. d = -1.4q Simplifying d = -1.4qSubproblem 2
Set the factor '(7d + -6q)' equal to zero and attempt to solve: Simplifying 7d + -6q = 0 Solving 7d + -6q = 0 Move all terms containing d to the left, all other terms to the right. Add '6q' to each side of the equation. 7d + -6q + 6q = 0 + 6q Combine like terms: -6q + 6q = 0 7d + 0 = 0 + 6q 7d = 0 + 6q Remove the zero: 7d = 6q Divide each side by '7'. d = 0.8571428571q Simplifying d = 0.8571428571qSolution
d = {-1.4q, 0.8571428571q}
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