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Simplifying 16d2 + 40d + 25 = 9 Reorder the terms: 25 + 40d + 16d2 = 9 Solving 25 + 40d + 16d2 = 9 Solving for variable 'd'. Reorder the terms: 25 + -9 + 40d + 16d2 = 9 + -9 Combine like terms: 25 + -9 = 16 16 + 40d + 16d2 = 9 + -9 Combine like terms: 9 + -9 = 0 16 + 40d + 16d2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(2 + 5d + 2d2) = 0 Factor a trinomial. 8((2 + d)(1 + 2d)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(2 + d)' equal to zero and attempt to solve: Simplifying 2 + d = 0 Solving 2 + d = 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 + d = 0 + -2 Combine like terms: 2 + -2 = 0 0 + d = 0 + -2 d = 0 + -2 Combine like terms: 0 + -2 = -2 d = -2 Simplifying d = -2Subproblem 2
Set the factor '(1 + 2d)' equal to zero and attempt to solve: Simplifying 1 + 2d = 0 Solving 1 + 2d = 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 + 2d = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2d = 0 + -1 2d = 0 + -1 Combine like terms: 0 + -1 = -1 2d = -1 Divide each side by '2'. d = -0.5 Simplifying d = -0.5Solution
d = {-2, -0.5}
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