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Simplifying d2 + -22d = -27 Reorder the terms: -22d + d2 = -27 Solving -22d + d2 = -27 Solving for variable 'd'. Reorder the terms: 27 + -22d + d2 = -27 + 27 Combine like terms: -27 + 27 = 0 27 + -22d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -22d + -27 + d2 = 0 + -27 Reorder the terms: 27 + -27 + -22d + d2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -22d + d2 = 0 + -27 -22d + d2 = 0 + -27 Combine like terms: 0 + -27 = -27 -22d + d2 = -27 The d term is -22d. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22d + 121 + d2 = -27 + 121 Reorder the terms: 121 + -22d + d2 = -27 + 121 Combine like terms: -27 + 121 = 94 121 + -22d + d2 = 94 Factor a perfect square on the left side: (d + -11)(d + -11) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (d + -11) equal to 9.695359715 and -9.695359715.Subproblem 1
d + -11 = 9.695359715 Simplifying d + -11 = 9.695359715 Reorder the terms: -11 + d = 9.695359715 Solving -11 + d = 9.695359715 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + d = 9.695359715 + 11 Combine like terms: -11 + 11 = 0 0 + d = 9.695359715 + 11 d = 9.695359715 + 11 Combine like terms: 9.695359715 + 11 = 20.695359715 d = 20.695359715 Simplifying d = 20.695359715Subproblem 2
d + -11 = -9.695359715 Simplifying d + -11 = -9.695359715 Reorder the terms: -11 + d = -9.695359715 Solving -11 + d = -9.695359715 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + d = -9.695359715 + 11 Combine like terms: -11 + 11 = 0 0 + d = -9.695359715 + 11 d = -9.695359715 + 11 Combine like terms: -9.695359715 + 11 = 1.304640285 d = 1.304640285 Simplifying d = 1.304640285Solution
The solution to the problem is based on the solutions from the subproblems. d = {20.695359715, 1.304640285}
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