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Simplifying 20w2 + -100wd + 125d2 = 0 Reorder the terms: -100dw + 125d2 + 20w2 = 0 Solving -100dw + 125d2 + 20w2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20dw + 25d2 + 4w2) = 0 Factor a trinomial. 5((5d + -2w)(5d + -2w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5d + -2w)' equal to zero and attempt to solve: Simplifying 5d + -2w = 0 Solving 5d + -2w = 0 Move all terms containing d to the left, all other terms to the right. Add '2w' to each side of the equation. 5d + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 5d + 0 = 0 + 2w 5d = 0 + 2w Remove the zero: 5d = 2w Divide each side by '5'. d = 0.4w Simplifying d = 0.4wSubproblem 2
Set the factor '(5d + -2w)' equal to zero and attempt to solve: Simplifying 5d + -2w = 0 Solving 5d + -2w = 0 Move all terms containing d to the left, all other terms to the right. Add '2w' to each side of the equation. 5d + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 5d + 0 = 0 + 2w 5d = 0 + 2w Remove the zero: 5d = 2w Divide each side by '5'. d = 0.4w Simplifying d = 0.4wSolution
d = {0.4w, 0.4w}
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