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Simplifying d2 + 18(d + 4) = 3 Reorder the terms: d2 + 18(4 + d) = 3 d2 + (4 * 18 + d * 18) = 3 d2 + (72 + 18d) = 3 Reorder the terms: 72 + 18d + d2 = 3 Solving 72 + 18d + d2 = 3 Solving for variable 'd'. Reorder the terms: 72 + -3 + 18d + d2 = 3 + -3 Combine like terms: 72 + -3 = 69 69 + 18d + d2 = 3 + -3 Combine like terms: 3 + -3 = 0 69 + 18d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-69' to each side of the equation. 69 + 18d + -69 + d2 = 0 + -69 Reorder the terms: 69 + -69 + 18d + d2 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + 18d + d2 = 0 + -69 18d + d2 = 0 + -69 Combine like terms: 0 + -69 = -69 18d + d2 = -69 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 = -69 + 81 Reorder the terms: 81 + 18d + d2 = -69 + 81 Combine like terms: -69 + 81 = 12 81 + 18d + d2 = 12 Factor a perfect square on the left side: (d + 9)(d + 9) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (d + 9) equal to 3.464101615 and -3.464101615.Subproblem 1
d + 9 = 3.464101615 Simplifying d + 9 = 3.464101615 Reorder the terms: 9 + d = 3.464101615 Solving 9 + d = 3.464101615 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 = 3.464101615 + -9 Combine like terms: 9 + -9 = 0 0 + d = 3.464101615 + -9 d = 3.464101615 + -9 Combine like terms: 3.464101615 + -9 = -5.535898385 d = -5.535898385 Simplifying d = -5.535898385Subproblem 2
d + 9 = -3.464101615 Simplifying d + 9 = -3.464101615 Reorder the terms: 9 + d = -3.464101615 Solving 9 + d = -3.464101615 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 = -3.464101615 + -9 Combine like terms: 9 + -9 = 0 0 + d = -3.464101615 + -9 d = -3.464101615 + -9 Combine like terms: -3.464101615 + -9 = -12.464101615 d = -12.464101615 Simplifying d = -12.464101615Solution
The solution to the problem is based on the solutions from the subproblems. d = {-5.535898385, -12.464101615}
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