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Simplifying d2 + -10d + 25 = 8 Reorder the terms: 25 + -10d + d2 = 8 Solving 25 + -10d + d2 = 8 Solving for variable 'd'. Reorder the terms: 25 + -8 + -10d + d2 = 8 + -8 Combine like terms: 25 + -8 = 17 17 + -10d + d2 = 8 + -8 Combine like terms: 8 + -8 = 0 17 + -10d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -10d + -17 + d2 = 0 + -17 Reorder the terms: 17 + -17 + -10d + d2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -10d + d2 = 0 + -17 -10d + d2 = 0 + -17 Combine like terms: 0 + -17 = -17 -10d + d2 = -17 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 = -17 + 25 Reorder the terms: 25 + -10d + d2 = -17 + 25 Combine like terms: -17 + 25 = 8 25 + -10d + d2 = 8 Factor a perfect square on the left side: (d + -5)(d + -5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (d + -5) equal to 2.828427125 and -2.828427125.Subproblem 1
d + -5 = 2.828427125 Simplifying d + -5 = 2.828427125 Reorder the terms: -5 + d = 2.828427125 Solving -5 + d = 2.828427125 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 = 2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + d = 2.828427125 + 5 d = 2.828427125 + 5 Combine like terms: 2.828427125 + 5 = 7.828427125 d = 7.828427125 Simplifying d = 7.828427125Subproblem 2
d + -5 = -2.828427125 Simplifying d + -5 = -2.828427125 Reorder the terms: -5 + d = -2.828427125 Solving -5 + d = -2.828427125 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 = -2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + d = -2.828427125 + 5 d = -2.828427125 + 5 Combine like terms: -2.828427125 + 5 = 2.171572875 d = 2.171572875 Simplifying d = 2.171572875Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.828427125, 2.171572875}
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