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Simplifying 2u2 + 9uv + -81v2 = 0 Reorder the terms: 9uv + 2u2 + -81v2 = 0 Solving 9uv + 2u2 + -81v2 = 0 Solving for variable 'u'. Factor a trinomial. (2u + -9v)(u + 9v) = 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 '(u + 9v)' equal to zero and attempt to solve: Simplifying u + 9v = 0 Solving u + 9v = 0 Move all terms containing u to the left, all other terms to the right. Add '-9v' to each side of the equation. u + 9v + -9v = 0 + -9v Combine like terms: 9v + -9v = 0 u + 0 = 0 + -9v u = 0 + -9v Remove the zero: u = -9v Simplifying u = -9vSolution
u = {4.5v, -9v}
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