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Simplifying d2 + 2d + -8 = 30 Reorder the terms: -8 + 2d + d2 = 30 Solving -8 + 2d + d2 = 30 Solving for variable 'd'. Reorder the terms: -8 + -30 + 2d + d2 = 30 + -30 Combine like terms: -8 + -30 = -38 -38 + 2d + d2 = 30 + -30 Combine like terms: 30 + -30 = 0 -38 + 2d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 2d + 38 + d2 = 0 + 38 Reorder the terms: -38 + 38 + 2d + d2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 2d + d2 = 0 + 38 2d + d2 = 0 + 38 Combine like terms: 0 + 38 = 38 2d + d2 = 38 The d term is 2d. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2d + 1 + d2 = 38 + 1 Reorder the terms: 1 + 2d + d2 = 38 + 1 Combine like terms: 38 + 1 = 39 1 + 2d + d2 = 39 Factor a perfect square on the left side: (d + 1)(d + 1) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (d + 1) equal to 6.244997998 and -6.244997998.Subproblem 1
d + 1 = 6.244997998 Simplifying d + 1 = 6.244997998 Reorder the terms: 1 + d = 6.244997998 Solving 1 + d = 6.244997998 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = 6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + d = 6.244997998 + -1 d = 6.244997998 + -1 Combine like terms: 6.244997998 + -1 = 5.244997998 d = 5.244997998 Simplifying d = 5.244997998Subproblem 2
d + 1 = -6.244997998 Simplifying d + 1 = -6.244997998 Reorder the terms: 1 + d = -6.244997998 Solving 1 + d = -6.244997998 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = -6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + d = -6.244997998 + -1 d = -6.244997998 + -1 Combine like terms: -6.244997998 + -1 = -7.244997998 d = -7.244997998 Simplifying d = -7.244997998Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.244997998, -7.244997998}
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