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Simplifying d2 + -8d + -45 = 0 Reorder the terms: -45 + -8d + d2 = 0 Solving -45 + -8d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -8d + 45 + d2 = 0 + 45 Reorder the terms: -45 + 45 + -8d + d2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -8d + d2 = 0 + 45 -8d + d2 = 0 + 45 Combine like terms: 0 + 45 = 45 -8d + d2 = 45 The d term is -8d. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8d + 16 + d2 = 45 + 16 Reorder the terms: 16 + -8d + d2 = 45 + 16 Combine like terms: 45 + 16 = 61 16 + -8d + d2 = 61 Factor a perfect square on the left side: (d + -4)(d + -4) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (d + -4) equal to 7.810249676 and -7.810249676.Subproblem 1
d + -4 = 7.810249676 Simplifying d + -4 = 7.810249676 Reorder the terms: -4 + d = 7.810249676 Solving -4 + d = 7.810249676 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = 7.810249676 + 4 Combine like terms: -4 + 4 = 0 0 + d = 7.810249676 + 4 d = 7.810249676 + 4 Combine like terms: 7.810249676 + 4 = 11.810249676 d = 11.810249676 Simplifying d = 11.810249676Subproblem 2
d + -4 = -7.810249676 Simplifying d + -4 = -7.810249676 Reorder the terms: -4 + d = -7.810249676 Solving -4 + d = -7.810249676 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = -7.810249676 + 4 Combine like terms: -4 + 4 = 0 0 + d = -7.810249676 + 4 d = -7.810249676 + 4 Combine like terms: -7.810249676 + 4 = -3.810249676 d = -3.810249676 Simplifying d = -3.810249676Solution
The solution to the problem is based on the solutions from the subproblems. d = {11.810249676, -3.810249676}
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