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Simplifying d2 + 60d + -300 = 0 Reorder the terms: -300 + 60d + d2 = 0 Solving -300 + 60d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 60d + 300 + d2 = 0 + 300 Reorder the terms: -300 + 300 + 60d + d2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 60d + d2 = 0 + 300 60d + d2 = 0 + 300 Combine like terms: 0 + 300 = 300 60d + d2 = 300 The d term is 60d. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60d + 900 + d2 = 300 + 900 Reorder the terms: 900 + 60d + d2 = 300 + 900 Combine like terms: 300 + 900 = 1200 900 + 60d + d2 = 1200 Factor a perfect square on the left side: (d + 30)(d + 30) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (d + 30) equal to 34.641016151 and -34.641016151.Subproblem 1
d + 30 = 34.641016151 Simplifying d + 30 = 34.641016151 Reorder the terms: 30 + d = 34.641016151 Solving 30 + d = 34.641016151 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + d = 34.641016151 + -30 Combine like terms: 30 + -30 = 0 0 + d = 34.641016151 + -30 d = 34.641016151 + -30 Combine like terms: 34.641016151 + -30 = 4.641016151 d = 4.641016151 Simplifying d = 4.641016151Subproblem 2
d + 30 = -34.641016151 Simplifying d + 30 = -34.641016151 Reorder the terms: 30 + d = -34.641016151 Solving 30 + d = -34.641016151 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + d = -34.641016151 + -30 Combine like terms: 30 + -30 = 0 0 + d = -34.641016151 + -30 d = -34.641016151 + -30 Combine like terms: -34.641016151 + -30 = -64.641016151 d = -64.641016151 Simplifying d = -64.641016151Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.641016151, -64.641016151}
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