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Simplifying d2 + 18(d + 4) = 9 Reorder the terms: d2 + 18(4 + d) = 9 d2 + (4 * 18 + d * 18) = 9 d2 + (72 + 18d) = 9 Reorder the terms: 72 + 18d + d2 = 9 Solving 72 + 18d + d2 = 9 Solving for variable 'd'. Reorder the terms: 72 + -9 + 18d + d2 = 9 + -9 Combine like terms: 72 + -9 = 63 63 + 18d + d2 = 9 + -9 Combine like terms: 9 + -9 = 0 63 + 18d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 18d + -63 + d2 = 0 + -63 Reorder the terms: 63 + -63 + 18d + d2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 18d + d2 = 0 + -63 18d + d2 = 0 + -63 Combine like terms: 0 + -63 = -63 18d + d2 = -63 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 = -63 + 81 Reorder the terms: 81 + 18d + d2 = -63 + 81 Combine like terms: -63 + 81 = 18 81 + 18d + d2 = 18 Factor a perfect square on the left side: (d + 9)(d + 9) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (d + 9) equal to 4.242640687 and -4.242640687.Subproblem 1
d + 9 = 4.242640687 Simplifying d + 9 = 4.242640687 Reorder the terms: 9 + d = 4.242640687 Solving 9 + d = 4.242640687 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 = 4.242640687 + -9 Combine like terms: 9 + -9 = 0 0 + d = 4.242640687 + -9 d = 4.242640687 + -9 Combine like terms: 4.242640687 + -9 = -4.757359313 d = -4.757359313 Simplifying d = -4.757359313Subproblem 2
d + 9 = -4.242640687 Simplifying d + 9 = -4.242640687 Reorder the terms: 9 + d = -4.242640687 Solving 9 + d = -4.242640687 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 = -4.242640687 + -9 Combine like terms: 9 + -9 = 0 0 + d = -4.242640687 + -9 d = -4.242640687 + -9 Combine like terms: -4.242640687 + -9 = -13.242640687 d = -13.242640687 Simplifying d = -13.242640687Solution
The solution to the problem is based on the solutions from the subproblems. d = {-4.757359313, -13.242640687}
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