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Simplifying d2 + 18(d + 4) = 29 Reorder the terms: d2 + 18(4 + d) = 29 d2 + (4 * 18 + d * 18) = 29 d2 + (72 + 18d) = 29 Reorder the terms: 72 + 18d + d2 = 29 Solving 72 + 18d + d2 = 29 Solving for variable 'd'. Reorder the terms: 72 + -29 + 18d + d2 = 29 + -29 Combine like terms: 72 + -29 = 43 43 + 18d + d2 = 29 + -29 Combine like terms: 29 + -29 = 0 43 + 18d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 18d + -43 + d2 = 0 + -43 Reorder the terms: 43 + -43 + 18d + d2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 18d + d2 = 0 + -43 18d + d2 = 0 + -43 Combine like terms: 0 + -43 = -43 18d + d2 = -43 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 = -43 + 81 Reorder the terms: 81 + 18d + d2 = -43 + 81 Combine like terms: -43 + 81 = 38 81 + 18d + d2 = 38 Factor a perfect square on the left side: (d + 9)(d + 9) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (d + 9) equal to 6.164414003 and -6.164414003.Subproblem 1
d + 9 = 6.164414003 Simplifying d + 9 = 6.164414003 Reorder the terms: 9 + d = 6.164414003 Solving 9 + d = 6.164414003 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 = 6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + d = 6.164414003 + -9 d = 6.164414003 + -9 Combine like terms: 6.164414003 + -9 = -2.835585997 d = -2.835585997 Simplifying d = -2.835585997Subproblem 2
d + 9 = -6.164414003 Simplifying d + 9 = -6.164414003 Reorder the terms: 9 + d = -6.164414003 Solving 9 + d = -6.164414003 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 = -6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + d = -6.164414003 + -9 d = -6.164414003 + -9 Combine like terms: -6.164414003 + -9 = -15.164414003 d = -15.164414003 Simplifying d = -15.164414003Solution
The solution to the problem is based on the solutions from the subproblems. d = {-2.835585997, -15.164414003}
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