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Simplifying 24d2 + 16d + -33 = 7 Reorder the terms: -33 + 16d + 24d2 = 7 Solving -33 + 16d + 24d2 = 7 Solving for variable 'd'. Reorder the terms: -33 + -7 + 16d + 24d2 = 7 + -7 Combine like terms: -33 + -7 = -40 -40 + 16d + 24d2 = 7 + -7 Combine like terms: 7 + -7 = 0 -40 + 16d + 24d2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + 2d + 3d2) = 0 Factor a trinomial. 8((-5 + -3d)(1 + -1d)) = 0 Ignore the factor 8.Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(1 + -1d)' equal to zero and attempt to solve: Simplifying 1 + -1d = 0 Solving 1 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1d = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1d = 0 + -1 -1d = 0 + -1 Combine like terms: 0 + -1 = -1 -1d = -1 Divide each side by '-1'. d = 1 Simplifying d = 1Solution
d = {-1.666666667, 1}
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