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Simplifying 10v2 + -33vw + 20w2 = 0 Reorder the terms: -33vw + 10v2 + 20w2 = 0 Solving -33vw + 10v2 + 20w2 = 0 Solving for variable 'v'. Factor a trinomial. (2v + -5w)(5v + -4w) = 0Subproblem 1
Set the factor '(2v + -5w)' equal to zero and attempt to solve: Simplifying 2v + -5w = 0 Solving 2v + -5w = 0 Move all terms containing v to the left, all other terms to the right. Add '5w' to each side of the equation. 2v + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 2v + 0 = 0 + 5w 2v = 0 + 5w Remove the zero: 2v = 5w Divide each side by '2'. v = 2.5w Simplifying v = 2.5wSubproblem 2
Set the factor '(5v + -4w)' equal to zero and attempt to solve: Simplifying 5v + -4w = 0 Solving 5v + -4w = 0 Move all terms containing v to the left, all other terms to the right. Add '4w' to each side of the equation. 5v + -4w + 4w = 0 + 4w Combine like terms: -4w + 4w = 0 5v + 0 = 0 + 4w 5v = 0 + 4w Remove the zero: 5v = 4w Divide each side by '5'. v = 0.8w Simplifying v = 0.8wSolution
v = {2.5w, 0.8w}
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