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Simplifying 12u2 + -76uv + 112v2 = 0 Reorder the terms: -76uv + 12u2 + 112v2 = 0 Solving -76uv + 12u2 + 112v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '4'. 4(-19uv + 3u2 + 28v2) = 0 Factor a trinomial. 4((u + -4v)(3u + -7v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(u + -4v)' equal to zero and attempt to solve: Simplifying u + -4v = 0 Solving u + -4v = 0 Move all terms containing u to the left, all other terms to the right. Add '4v' to each side of the equation. u + -4v + 4v = 0 + 4v Combine like terms: -4v + 4v = 0 u + 0 = 0 + 4v u = 0 + 4v Remove the zero: u = 4v Simplifying u = 4vSubproblem 2
Set the factor '(3u + -7v)' equal to zero and attempt to solve: Simplifying 3u + -7v = 0 Solving 3u + -7v = 0 Move all terms containing u to the left, all other terms to the right. Add '7v' to each side of the equation. 3u + -7v + 7v = 0 + 7v Combine like terms: -7v + 7v = 0 3u + 0 = 0 + 7v 3u = 0 + 7v Remove the zero: 3u = 7v Divide each side by '3'. u = 2.333333333v Simplifying u = 2.333333333vSolution
u = {4v, 2.333333333v}
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