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Simplifying d(d + -8) + -5 = 9(d + 2) + 1 Reorder the terms: d(-8 + d) + -5 = 9(d + 2) + 1 (-8 * d + d * d) + -5 = 9(d + 2) + 1 (-8d + d2) + -5 = 9(d + 2) + 1 Reorder the terms: -5 + -8d + d2 = 9(d + 2) + 1 Reorder the terms: -5 + -8d + d2 = 9(2 + d) + 1 -5 + -8d + d2 = (2 * 9 + d * 9) + 1 -5 + -8d + d2 = (18 + 9d) + 1 Reorder the terms: -5 + -8d + d2 = 18 + 1 + 9d Combine like terms: 18 + 1 = 19 -5 + -8d + d2 = 19 + 9d Solving -5 + -8d + d2 = 19 + 9d Solving for variable 'd'. Reorder the terms: -5 + -19 + -8d + -9d + d2 = 19 + 9d + -19 + -9d Combine like terms: -5 + -19 = -24 -24 + -8d + -9d + d2 = 19 + 9d + -19 + -9d Combine like terms: -8d + -9d = -17d -24 + -17d + d2 = 19 + 9d + -19 + -9d Reorder the terms: -24 + -17d + d2 = 19 + -19 + 9d + -9d Combine like terms: 19 + -19 = 0 -24 + -17d + d2 = 0 + 9d + -9d -24 + -17d + d2 = 9d + -9d Combine like terms: 9d + -9d = 0 -24 + -17d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -17d + 24 + d2 = 0 + 24 Reorder the terms: -24 + 24 + -17d + d2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -17d + d2 = 0 + 24 -17d + d2 = 0 + 24 Combine like terms: 0 + 24 = 24 -17d + d2 = 24 The d term is -17d. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17d + 72.25 + d2 = 24 + 72.25 Reorder the terms: 72.25 + -17d + d2 = 24 + 72.25 Combine like terms: 24 + 72.25 = 96.25 72.25 + -17d + d2 = 96.25 Factor a perfect square on the left side: (d + -8.5)(d + -8.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (d + -8.5) equal to 9.810708435 and -9.810708435.Subproblem 1
d + -8.5 = 9.810708435 Simplifying d + -8.5 = 9.810708435 Reorder the terms: -8.5 + d = 9.810708435 Solving -8.5 + d = 9.810708435 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + d = 9.810708435 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + d = 9.810708435 + 8.5 d = 9.810708435 + 8.5 Combine like terms: 9.810708435 + 8.5 = 18.310708435 d = 18.310708435 Simplifying d = 18.310708435Subproblem 2
d + -8.5 = -9.810708435 Simplifying d + -8.5 = -9.810708435 Reorder the terms: -8.5 + d = -9.810708435 Solving -8.5 + d = -9.810708435 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + d = -9.810708435 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + d = -9.810708435 + 8.5 d = -9.810708435 + 8.5 Combine like terms: -9.810708435 + 8.5 = -1.310708435 d = -1.310708435 Simplifying d = -1.310708435Solution
The solution to the problem is based on the solutions from the subproblems. d = {18.310708435, -1.310708435}
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