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Simplifying 84v2 + -34vw + -30w2 = 0 Reorder the terms: -34vw + 84v2 + -30w2 = 0 Solving -34vw + 84v2 + -30w2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17vw + 42v2 + -15w2) = 0 Factor a trinomial. 2((6v + -5w)(7v + 3w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6v + -5w)' equal to zero and attempt to solve: Simplifying 6v + -5w = 0 Solving 6v + -5w = 0 Move all terms containing v to the left, all other terms to the right. Add '5w' to each side of the equation. 6v + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 6v + 0 = 0 + 5w 6v = 0 + 5w Remove the zero: 6v = 5w Divide each side by '6'. v = 0.8333333333w Simplifying v = 0.8333333333wSubproblem 2
Set the factor '(7v + 3w)' equal to zero and attempt to solve: Simplifying 7v + 3w = 0 Solving 7v + 3w = 0 Move all terms containing v to the left, all other terms to the right. Add '-3w' to each side of the equation. 7v + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 7v + 0 = 0 + -3w 7v = 0 + -3w Remove the zero: 7v = -3w Divide each side by '7'. v = -0.4285714286w Simplifying v = -0.4285714286wSolution
v = {0.8333333333w, -0.4285714286w}
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