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Simplifying 6u2 + -31uv + 18v2 = 0 Reorder the terms: -31uv + 6u2 + 18v2 = 0 Solving -31uv + 6u2 + 18v2 = 0 Solving for variable 'u'. Factor a trinomial. (2u + -9v)(3u + -2v) = 0Subproblem 1
Set the factor '(2u + -9v)' equal to zero and attempt to solve: Simplifying 2u + -9v = 0 Solving 2u + -9v = 0 Move all terms containing u to the left, all other terms to the right. Add '9v' to each side of the equation. 2u + -9v + 9v = 0 + 9v Combine like terms: -9v + 9v = 0 2u + 0 = 0 + 9v 2u = 0 + 9v Remove the zero: 2u = 9v Divide each side by '2'. u = 4.5v Simplifying u = 4.5vSubproblem 2
Set the factor '(3u + -2v)' equal to zero and attempt to solve: Simplifying 3u + -2v = 0 Solving 3u + -2v = 0 Move all terms containing u to the left, all other terms to the right. Add '2v' to each side of the equation. 3u + -2v + 2v = 0 + 2v Combine like terms: -2v + 2v = 0 3u + 0 = 0 + 2v 3u = 0 + 2v Remove the zero: 3u = 2v Divide each side by '3'. u = 0.6666666667v Simplifying u = 0.6666666667vSolution
u = {4.5v, 0.6666666667v}
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