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Simplifying d2 + 10d + 18 = 0 Reorder the terms: 18 + 10d + d2 = 0 Solving 18 + 10d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 10d + -18 + d2 = 0 + -18 Reorder the terms: 18 + -18 + 10d + d2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 10d + d2 = 0 + -18 10d + d2 = 0 + -18 Combine like terms: 0 + -18 = -18 10d + d2 = -18 The d term is 10d. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10d + 25 + d2 = -18 + 25 Reorder the terms: 25 + 10d + d2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + 10d + d2 = 7 Factor a perfect square on the left side: (d + 5)(d + 5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (d + 5) equal to 2.645751311 and -2.645751311.Subproblem 1
d + 5 = 2.645751311 Simplifying d + 5 = 2.645751311 Reorder the terms: 5 + d = 2.645751311 Solving 5 + d = 2.645751311 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + d = 2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + d = 2.645751311 + -5 d = 2.645751311 + -5 Combine like terms: 2.645751311 + -5 = -2.354248689 d = -2.354248689 Simplifying d = -2.354248689Subproblem 2
d + 5 = -2.645751311 Simplifying d + 5 = -2.645751311 Reorder the terms: 5 + d = -2.645751311 Solving 5 + d = -2.645751311 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + d = -2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + d = -2.645751311 + -5 d = -2.645751311 + -5 Combine like terms: -2.645751311 + -5 = -7.645751311 d = -7.645751311 Simplifying d = -7.645751311Solution
The solution to the problem is based on the solutions from the subproblems. d = {-2.354248689, -7.645751311}
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