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Simplifying (4v + 7u) * x(4v + 7u) = 0 Reorder the terms: (7u + 4v) * x(4v + 7u) = 0 Reorder the terms: (7u + 4v) * x(7u + 4v) = 0 Reorder the terms for easier multiplication: x(7u + 4v)(7u + 4v) = 0 Multiply (7u + 4v) * (7u + 4v) x(7u * (7u + 4v) + 4v * (7u + 4v)) = 0 x((7u * 7u + 4v * 7u) + 4v * (7u + 4v)) = 0 Reorder the terms: x((28uv + 49u2) + 4v * (7u + 4v)) = 0 x((28uv + 49u2) + 4v * (7u + 4v)) = 0 x(28uv + 49u2 + (7u * 4v + 4v * 4v)) = 0 x(28uv + 49u2 + (28uv + 16v2)) = 0 Reorder the terms: x(28uv + 28uv + 49u2 + 16v2) = 0 Combine like terms: 28uv + 28uv = 56uv x(56uv + 49u2 + 16v2) = 0 (56uv * x + 49u2 * x + 16v2 * x) = 0 (56uvx + 49u2x + 16v2x) = 0 Solving 56uvx + 49u2x + 16v2x = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'x'. x(56uv + 49u2 + 16v2) = 0 Factor a trinomial. x((7u + 4v)(7u + 4v)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing u to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7u + 4v)' equal to zero and attempt to solve: Simplifying 7u + 4v = 0 Solving 7u + 4v = 0 Move all terms containing u to the left, all other terms to the right. Add '-4v' to each side of the equation. 7u + 4v + -4v = 0 + -4v Combine like terms: 4v + -4v = 0 7u + 0 = 0 + -4v 7u = 0 + -4v Remove the zero: 7u = -4v Divide each side by '7'. u = -0.5714285714v Simplifying u = -0.5714285714vSubproblem 3
Set the factor '(7u + 4v)' equal to zero and attempt to solve: Simplifying 7u + 4v = 0 Solving 7u + 4v = 0 Move all terms containing u to the left, all other terms to the right. Add '-4v' to each side of the equation. 7u + 4v + -4v = 0 + -4v Combine like terms: 4v + -4v = 0 7u + 0 = 0 + -4v 7u = 0 + -4v Remove the zero: 7u = -4v Divide each side by '7'. u = -0.5714285714v Simplifying u = -0.5714285714vSolution
u = {-0.5714285714v, -0.5714285714v}
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