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Simplifying 50w2 + 40wd + 8d2 = 0 Reorder the terms: 40dw + 8d2 + 50w2 = 0 Solving 40dw + 8d2 + 50w2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(20dw + 4d2 + 25w2) = 0 Factor a trinomial. 2((2d + 5w)(2d + 5w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2d + 5w)' equal to zero and attempt to solve: Simplifying 2d + 5w = 0 Solving 2d + 5w = 0 Move all terms containing d to the left, all other terms to the right. Add '-5w' to each side of the equation. 2d + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 2d + 0 = 0 + -5w 2d = 0 + -5w Remove the zero: 2d = -5w Divide each side by '2'. d = -2.5w Simplifying d = -2.5wSubproblem 2
Set the factor '(2d + 5w)' equal to zero and attempt to solve: Simplifying 2d + 5w = 0 Solving 2d + 5w = 0 Move all terms containing d to the left, all other terms to the right. Add '-5w' to each side of the equation. 2d + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 2d + 0 = 0 + -5w 2d = 0 + -5w Remove the zero: 2d = -5w Divide each side by '2'. d = -2.5w Simplifying d = -2.5wSolution
d = {-2.5w, -2.5w}
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