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Simplifying 36u2 + 4v2 + 24uv = 0 Reorder the terms: 24uv + 36u2 + 4v2 = 0 Solving 24uv + 36u2 + 4v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '4'. 4(6uv + 9u2 + v2) = 0 Factor a trinomial. 4((3u + v)(3u + v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3u + v)' equal to zero and attempt to solve: Simplifying 3u + v = 0 Solving 3u + v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. 3u + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 3u + 0 = 0 + -1v 3u = 0 + -1v Remove the zero: 3u = -1v Divide each side by '3'. u = -0.3333333333v Simplifying u = -0.3333333333vSubproblem 2
Set the factor '(3u + v)' equal to zero and attempt to solve: Simplifying 3u + v = 0 Solving 3u + v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. 3u + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 3u + 0 = 0 + -1v 3u = 0 + -1v Remove the zero: 3u = -1v Divide each side by '3'. u = -0.3333333333v Simplifying u = -0.3333333333vSolution
u = {-0.3333333333v, -0.3333333333v}
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