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Simplifying -45u2 + 150uv + -125v2 = 0 Reorder the terms: 150uv + -45u2 + -125v2 = 0 Solving 150uv + -45u2 + -125v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '5'. 5(30uv + -9u2 + -25v2) = 0 Factor a trinomial. 5((-3u + 5v)(3u + -5v)) = 0 Ignore the factor 5.Subproblem 1
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 = 1.666666667vSubproblem 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 = {1.666666667v, 1.666666667v}
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