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Simplifying d2 = 8d + 16 Reorder the terms: d2 = 16 + 8d Solving d2 = 16 + 8d Solving for variable 'd'. Reorder the terms: -16 + -8d + d2 = 16 + 8d + -16 + -8d Reorder the terms: -16 + -8d + d2 = 16 + -16 + 8d + -8d Combine like terms: 16 + -16 = 0 -16 + -8d + d2 = 0 + 8d + -8d -16 + -8d + d2 = 8d + -8d Combine like terms: 8d + -8d = 0 -16 + -8d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -8d + 16 + d2 = 0 + 16 Reorder the terms: -16 + 16 + -8d + d2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8d + d2 = 0 + 16 -8d + d2 = 0 + 16 Combine like terms: 0 + 16 = 16 -8d + d2 = 16 The d term is -8d. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8d + 16 + d2 = 16 + 16 Reorder the terms: 16 + -8d + d2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8d + d2 = 32 Factor a perfect square on the left side: (d + -4)(d + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (d + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
d + -4 = 5.656854249 Simplifying d + -4 = 5.656854249 Reorder the terms: -4 + d = 5.656854249 Solving -4 + d = 5.656854249 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + d = 5.656854249 + 4 d = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 d = 9.656854249 Simplifying d = 9.656854249Subproblem 2
d + -4 = -5.656854249 Simplifying d + -4 = -5.656854249 Reorder the terms: -4 + d = -5.656854249 Solving -4 + d = -5.656854249 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + d = -5.656854249 + 4 d = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 d = -1.656854249 Simplifying d = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. d = {9.656854249, -1.656854249}
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