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Simplifying 2u2 + 5uv + 2v2 = 0 Reorder the terms: 5uv + 2u2 + 2v2 = 0 Solving 5uv + 2u2 + 2v2 = 0 Solving for variable 'u'. Factor a trinomial. (2u + v)(u + 2v) = 0Subproblem 1
Set the factor '(2u + v)' equal to zero and attempt to solve: Simplifying 2u + v = 0 Solving 2u + v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. 2u + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 2u + 0 = 0 + -1v 2u = 0 + -1v Remove the zero: 2u = -1v Divide each side by '2'. u = -0.5v Simplifying u = -0.5vSubproblem 2
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 = -2vSolution
u = {-0.5v, -2v}
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