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Simplifying (8d + -1)(8d + -1) = 81 Reorder the terms: (-1 + 8d)(8d + -1) = 81 Reorder the terms: (-1 + 8d)(-1 + 8d) = 81 Multiply (-1 + 8d) * (-1 + 8d) (-1(-1 + 8d) + 8d * (-1 + 8d)) = 81 ((-1 * -1 + 8d * -1) + 8d * (-1 + 8d)) = 81 ((1 + -8d) + 8d * (-1 + 8d)) = 81 (1 + -8d + (-1 * 8d + 8d * 8d)) = 81 (1 + -8d + (-8d + 64d2)) = 81 Combine like terms: -8d + -8d = -16d (1 + -16d + 64d2) = 81 Solving 1 + -16d + 64d2 = 81 Solving for variable 'd'. Reorder the terms: 1 + -81 + -16d + 64d2 = 81 + -81 Combine like terms: 1 + -81 = -80 -80 + -16d + 64d2 = 81 + -81 Combine like terms: 81 + -81 = 0 -80 + -16d + 64d2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-5 + -1d + 4d2) = 0 Factor a trinomial. 16((-1 + -1d)(5 + -4d)) = 0 Ignore the factor 16.Subproblem 1
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 = -1Subproblem 2
Set the factor '(5 + -4d)' equal to zero and attempt to solve: Simplifying 5 + -4d = 0 Solving 5 + -4d = 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 + -4d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4d = 0 + -5 -4d = 0 + -5 Combine like terms: 0 + -5 = -5 -4d = -5 Divide each side by '-4'. d = 1.25 Simplifying d = 1.25Solution
d = {-1, 1.25}
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