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Simplifying 8000 = -5d2 + 4500d Reorder the terms: 8000 = 4500d + -5d2 Solving 8000 = 4500d + -5d2 Solving for variable 'd'. Reorder the terms: 8000 + -4500d + 5d2 = 4500d + -4500d + -5d2 + 5d2 Combine like terms: 4500d + -4500d = 0 8000 + -4500d + 5d2 = 0 + -5d2 + 5d2 8000 + -4500d + 5d2 = -5d2 + 5d2 Combine like terms: -5d2 + 5d2 = 0 8000 + -4500d + 5d2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1600 + -900d + d2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1600 + -900d + d2)' equal to zero and attempt to solve: Simplifying 1600 + -900d + d2 = 0 Solving 1600 + -900d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + -900d + -1600 + d2 = 0 + -1600 Reorder the terms: 1600 + -1600 + -900d + d2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + -900d + d2 = 0 + -1600 -900d + d2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 -900d + d2 = -1600 The d term is -900d. Take half its coefficient (-450). Square it (202500) and add it to both sides. Add '202500' to each side of the equation. -900d + 202500 + d2 = -1600 + 202500 Reorder the terms: 202500 + -900d + d2 = -1600 + 202500 Combine like terms: -1600 + 202500 = 200900 202500 + -900d + d2 = 200900 Factor a perfect square on the left side: (d + -450)(d + -450) = 200900 Calculate the square root of the right side: 448.21869662 Break this problem into two subproblems by setting (d + -450) equal to 448.21869662 and -448.21869662.Subproblem 1
d + -450 = 448.21869662 Simplifying d + -450 = 448.21869662 Reorder the terms: -450 + d = 448.21869662 Solving -450 + d = 448.21869662 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + d = 448.21869662 + 450 Combine like terms: -450 + 450 = 0 0 + d = 448.21869662 + 450 d = 448.21869662 + 450 Combine like terms: 448.21869662 + 450 = 898.21869662 d = 898.21869662 Simplifying d = 898.21869662Subproblem 2
d + -450 = -448.21869662 Simplifying d + -450 = -448.21869662 Reorder the terms: -450 + d = -448.21869662 Solving -450 + d = -448.21869662 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + d = -448.21869662 + 450 Combine like terms: -450 + 450 = 0 0 + d = -448.21869662 + 450 d = -448.21869662 + 450 Combine like terms: -448.21869662 + 450 = 1.78130338 d = 1.78130338 Simplifying d = 1.78130338Solution
The solution to the problem is based on the solutions from the subproblems. d = {898.21869662, 1.78130338}Solution
d = {898.21869662, 1.78130338}
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