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Simplifying d2 + 22d + 121 = 12 Reorder the terms: 121 + 22d + d2 = 12 Solving 121 + 22d + d2 = 12 Solving for variable 'd'. Reorder the terms: 121 + -12 + 22d + d2 = 12 + -12 Combine like terms: 121 + -12 = 109 109 + 22d + d2 = 12 + -12 Combine like terms: 12 + -12 = 0 109 + 22d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-109' to each side of the equation. 109 + 22d + -109 + d2 = 0 + -109 Reorder the terms: 109 + -109 + 22d + d2 = 0 + -109 Combine like terms: 109 + -109 = 0 0 + 22d + d2 = 0 + -109 22d + d2 = 0 + -109 Combine like terms: 0 + -109 = -109 22d + d2 = -109 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 = -109 + 121 Reorder the terms: 121 + 22d + d2 = -109 + 121 Combine like terms: -109 + 121 = 12 121 + 22d + d2 = 12 Factor a perfect square on the left side: (d + 11)(d + 11) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (d + 11) equal to 3.464101615 and -3.464101615.Subproblem 1
d + 11 = 3.464101615 Simplifying d + 11 = 3.464101615 Reorder the terms: 11 + d = 3.464101615 Solving 11 + d = 3.464101615 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 = 3.464101615 + -11 Combine like terms: 11 + -11 = 0 0 + d = 3.464101615 + -11 d = 3.464101615 + -11 Combine like terms: 3.464101615 + -11 = -7.535898385 d = -7.535898385 Simplifying d = -7.535898385Subproblem 2
d + 11 = -3.464101615 Simplifying d + 11 = -3.464101615 Reorder the terms: 11 + d = -3.464101615 Solving 11 + d = -3.464101615 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 = -3.464101615 + -11 Combine like terms: 11 + -11 = 0 0 + d = -3.464101615 + -11 d = -3.464101615 + -11 Combine like terms: -3.464101615 + -11 = -14.464101615 d = -14.464101615 Simplifying d = -14.464101615Solution
The solution to the problem is based on the solutions from the subproblems. d = {-7.535898385, -14.464101615}
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