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Simplifying 2d2 + 8d + -18 = d2 + d Reorder the terms: -18 + 8d + 2d2 = d2 + d Reorder the terms: -18 + 8d + 2d2 = d + d2 Solving -18 + 8d + 2d2 = d + d2 Solving for variable 'd'. Reorder the terms: -18 + 8d + -1d + 2d2 + -1d2 = d + d2 + -1d + -1d2 Combine like terms: 8d + -1d = 7d -18 + 7d + 2d2 + -1d2 = d + d2 + -1d + -1d2 Combine like terms: 2d2 + -1d2 = 1d2 -18 + 7d + 1d2 = d + d2 + -1d + -1d2 Reorder the terms: -18 + 7d + 1d2 = d + -1d + d2 + -1d2 Combine like terms: d + -1d = 0 -18 + 7d + 1d2 = 0 + d2 + -1d2 -18 + 7d + 1d2 = d2 + -1d2 Combine like terms: d2 + -1d2 = 0 -18 + 7d + 1d2 = 0 Factor a trinomial. (-9 + -1d)(2 + -1d) = 0Subproblem 1
Set the factor '(-9 + -1d)' equal to zero and attempt to solve: Simplifying -9 + -1d = 0 Solving -9 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1d = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1d = 0 + 9 -1d = 0 + 9 Combine like terms: 0 + 9 = 9 -1d = 9 Divide each side by '-1'. d = -9 Simplifying d = -9Subproblem 2
Set the factor '(2 + -1d)' equal to zero and attempt to solve: Simplifying 2 + -1d = 0 Solving 2 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1d = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1d = 0 + -2 -1d = 0 + -2 Combine like terms: 0 + -2 = -2 -1d = -2 Divide each side by '-1'. d = 2 Simplifying d = 2Solution
d = {-9, 2}
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