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Simplifying w2 + 7wd + -18d2 = 0 Reorder the terms: 7dw + -18d2 + w2 = 0 Solving 7dw + -18d2 + w2 = 0 Solving for variable 'd'. Factor a trinomial. (-9d + -1w)(2d + -1w) = 0Subproblem 1
Set the factor '(-9d + -1w)' equal to zero and attempt to solve: Simplifying -9d + -1w = 0 Solving -9d + -1w = 0 Move all terms containing d to the left, all other terms to the right. Add 'w' to each side of the equation. -9d + -1w + w = 0 + w Combine like terms: -1w + w = 0 -9d + 0 = 0 + w -9d = 0 + w Remove the zero: -9d = w Divide each side by '-9'. d = -0.1111111111w Simplifying d = -0.1111111111wSubproblem 2
Set the factor '(2d + -1w)' equal to zero and attempt to solve: Simplifying 2d + -1w = 0 Solving 2d + -1w = 0 Move all terms containing d to the left, all other terms to the right. Add 'w' to each side of the equation. 2d + -1w + w = 0 + w Combine like terms: -1w + w = 0 2d + 0 = 0 + w 2d = 0 + w Remove the zero: 2d = w Divide each side by '2'. d = 0.5w Simplifying d = 0.5wSolution
d = {-0.1111111111w, 0.5w}
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