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Simplifying 0 = d2 + -900d + -12600 Reorder the terms: 0 = -12600 + -900d + d2 Solving 0 = -12600 + -900d + d2 Solving for variable 'd'. Combine like terms: 0 + 12600 = 12600 12600 + 900d + -1d2 = -12600 + -900d + d2 + 12600 + 900d + -1d2 Reorder the terms: 12600 + 900d + -1d2 = -12600 + 12600 + -900d + 900d + d2 + -1d2 Combine like terms: -12600 + 12600 = 0 12600 + 900d + -1d2 = 0 + -900d + 900d + d2 + -1d2 12600 + 900d + -1d2 = -900d + 900d + d2 + -1d2 Combine like terms: -900d + 900d = 0 12600 + 900d + -1d2 = 0 + d2 + -1d2 12600 + 900d + -1d2 = d2 + -1d2 Combine like terms: d2 + -1d2 = 0 12600 + 900d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12600 + -900d + d2 = 0 Move the constant term to the right: Add '12600' to each side of the equation. -12600 + -900d + 12600 + d2 = 0 + 12600 Reorder the terms: -12600 + 12600 + -900d + d2 = 0 + 12600 Combine like terms: -12600 + 12600 = 0 0 + -900d + d2 = 0 + 12600 -900d + d2 = 0 + 12600 Combine like terms: 0 + 12600 = 12600 -900d + d2 = 12600 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 = 12600 + 202500 Reorder the terms: 202500 + -900d + d2 = 12600 + 202500 Combine like terms: 12600 + 202500 = 215100 202500 + -900d + d2 = 215100 Factor a perfect square on the left side: (d + -450)(d + -450) = 215100 Calculate the square root of the right side: 463.788745012 Break this problem into two subproblems by setting (d + -450) equal to 463.788745012 and -463.788745012.Subproblem 1
d + -450 = 463.788745012 Simplifying d + -450 = 463.788745012 Reorder the terms: -450 + d = 463.788745012 Solving -450 + d = 463.788745012 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 = 463.788745012 + 450 Combine like terms: -450 + 450 = 0 0 + d = 463.788745012 + 450 d = 463.788745012 + 450 Combine like terms: 463.788745012 + 450 = 913.788745012 d = 913.788745012 Simplifying d = 913.788745012Subproblem 2
d + -450 = -463.788745012 Simplifying d + -450 = -463.788745012 Reorder the terms: -450 + d = -463.788745012 Solving -450 + d = -463.788745012 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 = -463.788745012 + 450 Combine like terms: -450 + 450 = 0 0 + d = -463.788745012 + 450 d = -463.788745012 + 450 Combine like terms: -463.788745012 + 450 = -13.788745012 d = -13.788745012 Simplifying d = -13.788745012Solution
The solution to the problem is based on the solutions from the subproblems. d = {913.788745012, -13.788745012}
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