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Simplifying 25w2 + 20wd + -25dw + -20d2 = 0 Reorder the terms: 20dw + -25dw + -20d2 + 25w2 = 0 Combine like terms: 20dw + -25dw = -5dw -5dw + -20d2 + 25w2 = 0 Solving -5dw + -20d2 + 25w2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1dw + -4d2 + 5w2) = 0 Factor a trinomial. 5((-4d + -5w)(d + -1w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4d + -5w)' equal to zero and attempt to solve: Simplifying -4d + -5w = 0 Solving -4d + -5w = 0 Move all terms containing d to the left, all other terms to the right. Add '5w' to each side of the equation. -4d + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 -4d + 0 = 0 + 5w -4d = 0 + 5w Remove the zero: -4d = 5w Divide each side by '-4'. d = -1.25w Simplifying d = -1.25wSubproblem 2
Set the factor '(d + -1w)' equal to zero and attempt to solve: Simplifying d + -1w = 0 Solving d + -1w = 0 Move all terms containing d to the left, all other terms to the right. Add 'w' to each side of the equation. d + -1w + w = 0 + w Combine like terms: -1w + w = 0 d + 0 = 0 + w d = 0 + w Remove the zero: d = w Simplifying d = wSolution
d = {-1.25w, w}
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