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Simplifying d2 + -18d + 68 = 0 Reorder the terms: 68 + -18d + d2 = 0 Solving 68 + -18d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + -18d + -68 + d2 = 0 + -68 Reorder the terms: 68 + -68 + -18d + d2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -18d + d2 = 0 + -68 -18d + d2 = 0 + -68 Combine like terms: 0 + -68 = -68 -18d + d2 = -68 The d term is -18d. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18d + 81 + d2 = -68 + 81 Reorder the terms: 81 + -18d + d2 = -68 + 81 Combine like terms: -68 + 81 = 13 81 + -18d + d2 = 13 Factor a perfect square on the left side: (d + -9)(d + -9) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (d + -9) equal to 3.605551275 and -3.605551275.Subproblem 1
d + -9 = 3.605551275 Simplifying d + -9 = 3.605551275 Reorder the terms: -9 + d = 3.605551275 Solving -9 + d = 3.605551275 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + d = 3.605551275 + 9 Combine like terms: -9 + 9 = 0 0 + d = 3.605551275 + 9 d = 3.605551275 + 9 Combine like terms: 3.605551275 + 9 = 12.605551275 d = 12.605551275 Simplifying d = 12.605551275Subproblem 2
d + -9 = -3.605551275 Simplifying d + -9 = -3.605551275 Reorder the terms: -9 + d = -3.605551275 Solving -9 + d = -3.605551275 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + d = -3.605551275 + 9 Combine like terms: -9 + 9 = 0 0 + d = -3.605551275 + 9 d = -3.605551275 + 9 Combine like terms: -3.605551275 + 9 = 5.394448725 d = 5.394448725 Simplifying d = 5.394448725Solution
The solution to the problem is based on the solutions from the subproblems. d = {12.605551275, 5.394448725}
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