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Simplifying 21d + 6d2 = 35 + 10d Solving 21d + 6d2 = 35 + 10d Solving for variable 'd'. Reorder the terms: -35 + 21d + -10d + 6d2 = 35 + 10d + -35 + -10d Combine like terms: 21d + -10d = 11d -35 + 11d + 6d2 = 35 + 10d + -35 + -10d Reorder the terms: -35 + 11d + 6d2 = 35 + -35 + 10d + -10d Combine like terms: 35 + -35 = 0 -35 + 11d + 6d2 = 0 + 10d + -10d -35 + 11d + 6d2 = 10d + -10d Combine like terms: 10d + -10d = 0 -35 + 11d + 6d2 = 0 Factor a trinomial. (-7 + -2d)(5 + -3d) = 0Subproblem 1
Set the factor '(-7 + -2d)' equal to zero and attempt to solve: Simplifying -7 + -2d = 0 Solving -7 + -2d = 0 Move all terms containing d to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2d = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2d = 0 + 7 -2d = 0 + 7 Combine like terms: 0 + 7 = 7 -2d = 7 Divide each side by '-2'. d = -3.5 Simplifying d = -3.5Subproblem 2
Set the factor '(5 + -3d)' equal to zero and attempt to solve: Simplifying 5 + -3d = 0 Solving 5 + -3d = 0 Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3d = 0 + -5 -3d = 0 + -5 Combine like terms: 0 + -5 = -5 -3d = -5 Divide each side by '-3'. d = 1.666666667 Simplifying d = 1.666666667Solution
d = {-3.5, 1.666666667}
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