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Simplifying (4u + 9v)(4u + 9v) = 0 Multiply (4u + 9v) * (4u + 9v) (4u * (4u + 9v) + 9v * (4u + 9v)) = 0 ((4u * 4u + 9v * 4u) + 9v * (4u + 9v)) = 0 Reorder the terms: ((36uv + 16u2) + 9v * (4u + 9v)) = 0 ((36uv + 16u2) + 9v * (4u + 9v)) = 0 (36uv + 16u2 + (4u * 9v + 9v * 9v)) = 0 (36uv + 16u2 + (36uv + 81v2)) = 0 Reorder the terms: (36uv + 36uv + 16u2 + 81v2) = 0 Combine like terms: 36uv + 36uv = 72uv (72uv + 16u2 + 81v2) = 0 Solving 72uv + 16u2 + 81v2 = 0 Solving for variable 'u'. Factor a trinomial. (4u + 9v)(4u + 9v) = 0Subproblem 1
Set the factor '(4u + 9v)' equal to zero and attempt to solve: Simplifying 4u + 9v = 0 Solving 4u + 9v = 0 Move all terms containing u to the left, all other terms to the right. Add '-9v' to each side of the equation. 4u + 9v + -9v = 0 + -9v Combine like terms: 9v + -9v = 0 4u + 0 = 0 + -9v 4u = 0 + -9v Remove the zero: 4u = -9v Divide each side by '4'. u = -2.25v Simplifying u = -2.25vSubproblem 2
Set the factor '(4u + 9v)' equal to zero and attempt to solve: Simplifying 4u + 9v = 0 Solving 4u + 9v = 0 Move all terms containing u to the left, all other terms to the right. Add '-9v' to each side of the equation. 4u + 9v + -9v = 0 + -9v Combine like terms: 9v + -9v = 0 4u + 0 = 0 + -9v 4u = 0 + -9v Remove the zero: 4u = -9v Divide each side by '4'. u = -2.25v Simplifying u = -2.25vSolution
u = {-2.25v, -2.25v}
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