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Simplifying d2 + -22d = 31 Reorder the terms: -22d + d2 = 31 Solving -22d + d2 = 31 Solving for variable 'd'. Reorder the terms: -31 + -22d + d2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + -22d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -22d + 31 + d2 = 0 + 31 Reorder the terms: -31 + 31 + -22d + d2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -22d + d2 = 0 + 31 -22d + d2 = 0 + 31 Combine like terms: 0 + 31 = 31 -22d + d2 = 31 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 = 31 + 121 Reorder the terms: 121 + -22d + d2 = 31 + 121 Combine like terms: 31 + 121 = 152 121 + -22d + d2 = 152 Factor a perfect square on the left side: (d + -11)(d + -11) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (d + -11) equal to 12.328828006 and -12.328828006.Subproblem 1
d + -11 = 12.328828006 Simplifying d + -11 = 12.328828006 Reorder the terms: -11 + d = 12.328828006 Solving -11 + d = 12.328828006 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 = 12.328828006 + 11 Combine like terms: -11 + 11 = 0 0 + d = 12.328828006 + 11 d = 12.328828006 + 11 Combine like terms: 12.328828006 + 11 = 23.328828006 d = 23.328828006 Simplifying d = 23.328828006Subproblem 2
d + -11 = -12.328828006 Simplifying d + -11 = -12.328828006 Reorder the terms: -11 + d = -12.328828006 Solving -11 + d = -12.328828006 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 = -12.328828006 + 11 Combine like terms: -11 + 11 = 0 0 + d = -12.328828006 + 11 d = -12.328828006 + 11 Combine like terms: -12.328828006 + 11 = -1.328828006 d = -1.328828006 Simplifying d = -1.328828006Solution
The solution to the problem is based on the solutions from the subproblems. d = {23.328828006, -1.328828006}
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