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Simplifying d2 + 10d + 25 = 15 Reorder the terms: 25 + 10d + d2 = 15 Solving 25 + 10d + d2 = 15 Solving for variable 'd'. Reorder the terms: 25 + -15 + 10d + d2 = 15 + -15 Combine like terms: 25 + -15 = 10 10 + 10d + d2 = 15 + -15 Combine like terms: 15 + -15 = 0 10 + 10d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 10d + -10 + d2 = 0 + -10 Reorder the terms: 10 + -10 + 10d + d2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 10d + d2 = 0 + -10 10d + d2 = 0 + -10 Combine like terms: 0 + -10 = -10 10d + d2 = -10 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 = -10 + 25 Reorder the terms: 25 + 10d + d2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + 10d + d2 = 15 Factor a perfect square on the left side: (d + 5)(d + 5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (d + 5) equal to 3.872983346 and -3.872983346.Subproblem 1
d + 5 = 3.872983346 Simplifying d + 5 = 3.872983346 Reorder the terms: 5 + d = 3.872983346 Solving 5 + d = 3.872983346 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 = 3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + d = 3.872983346 + -5 d = 3.872983346 + -5 Combine like terms: 3.872983346 + -5 = -1.127016654 d = -1.127016654 Simplifying d = -1.127016654Subproblem 2
d + 5 = -3.872983346 Simplifying d + 5 = -3.872983346 Reorder the terms: 5 + d = -3.872983346 Solving 5 + d = -3.872983346 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 = -3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + d = -3.872983346 + -5 d = -3.872983346 + -5 Combine like terms: -3.872983346 + -5 = -8.872983346 d = -8.872983346 Simplifying d = -8.872983346Solution
The solution to the problem is based on the solutions from the subproblems. d = {-1.127016654, -8.872983346}
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