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Simplifying 6u2 + -22uv + 20v2 = 0 Reorder the terms: -22uv + 6u2 + 20v2 = 0 Solving -22uv + 6u2 + 20v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11uv + 3u2 + 10v2) = 0 Factor a trinomial. 2((u + -2v)(3u + -5v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(u + -2v)' equal to zero and attempt to solve: Simplifying u + -2v = 0 Solving u + -2v = 0 Move all terms containing u to the left, all other terms to the right. Add '2v' to each side of the equation. u + -2v + 2v = 0 + 2v Combine like terms: -2v + 2v = 0 u + 0 = 0 + 2v u = 0 + 2v Remove the zero: u = 2v Simplifying u = 2vSubproblem 2
Set the factor '(3u + -5v)' equal to zero and attempt to solve: Simplifying 3u + -5v = 0 Solving 3u + -5v = 0 Move all terms containing u to the left, all other terms to the right. Add '5v' to each side of the equation. 3u + -5v + 5v = 0 + 5v Combine like terms: -5v + 5v = 0 3u + 0 = 0 + 5v 3u = 0 + 5v Remove the zero: 3u = 5v Divide each side by '3'. u = 1.666666667v Simplifying u = 1.666666667vSolution
u = {2v, 1.666666667v}
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