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Simplifying d2 + 22d + 121 = 18 Reorder the terms: 121 + 22d + d2 = 18 Solving 121 + 22d + d2 = 18 Solving for variable 'd'. Reorder the terms: 121 + -18 + 22d + d2 = 18 + -18 Combine like terms: 121 + -18 = 103 103 + 22d + d2 = 18 + -18 Combine like terms: 18 + -18 = 0 103 + 22d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-103' to each side of the equation. 103 + 22d + -103 + d2 = 0 + -103 Reorder the terms: 103 + -103 + 22d + d2 = 0 + -103 Combine like terms: 103 + -103 = 0 0 + 22d + d2 = 0 + -103 22d + d2 = 0 + -103 Combine like terms: 0 + -103 = -103 22d + d2 = -103 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 = -103 + 121 Reorder the terms: 121 + 22d + d2 = -103 + 121 Combine like terms: -103 + 121 = 18 121 + 22d + d2 = 18 Factor a perfect square on the left side: (d + 11)(d + 11) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (d + 11) equal to 4.242640687 and -4.242640687.Subproblem 1
d + 11 = 4.242640687 Simplifying d + 11 = 4.242640687 Reorder the terms: 11 + d = 4.242640687 Solving 11 + d = 4.242640687 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 = 4.242640687 + -11 Combine like terms: 11 + -11 = 0 0 + d = 4.242640687 + -11 d = 4.242640687 + -11 Combine like terms: 4.242640687 + -11 = -6.757359313 d = -6.757359313 Simplifying d = -6.757359313Subproblem 2
d + 11 = -4.242640687 Simplifying d + 11 = -4.242640687 Reorder the terms: 11 + d = -4.242640687 Solving 11 + d = -4.242640687 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 = -4.242640687 + -11 Combine like terms: 11 + -11 = 0 0 + d = -4.242640687 + -11 d = -4.242640687 + -11 Combine like terms: -4.242640687 + -11 = -15.242640687 d = -15.242640687 Simplifying d = -15.242640687Solution
The solution to the problem is based on the solutions from the subproblems. d = {-6.757359313, -15.242640687}
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