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Simplifying 168q2 + -57qd + -45d2 = 0 Reorder the terms: -57dq + -45d2 + 168q2 = 0 Solving -57dq + -45d2 + 168q2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '3'. 3(-19dq + -15d2 + 56q2) = 0 Factor a trinomial. 3((-3d + -8q)(5d + -7q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3d + -8q)' equal to zero and attempt to solve: Simplifying -3d + -8q = 0 Solving -3d + -8q = 0 Move all terms containing d to the left, all other terms to the right. Add '8q' to each side of the equation. -3d + -8q + 8q = 0 + 8q Combine like terms: -8q + 8q = 0 -3d + 0 = 0 + 8q -3d = 0 + 8q Remove the zero: -3d = 8q Divide each side by '-3'. d = -2.666666667q Simplifying d = -2.666666667qSubproblem 2
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 = 1.4qSolution
d = {-2.666666667q, 1.4q}
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