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Simplifying 3900d + 156 + -25.32d2 = 0 Reorder the terms: 156 + 3900d + -25.32d2 = 0 Solving 156 + 3900d + -25.32d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by -25.32 the coefficient of the squared term: Divide each side by '-25.32'. -6.161137441 + -154.028436d + d2 = 0 Move the constant term to the right: Add '6.161137441' to each side of the equation. -6.161137441 + -154.028436d + 6.161137441 + d2 = 0 + 6.161137441 Reorder the terms: -6.161137441 + 6.161137441 + -154.028436d + d2 = 0 + 6.161137441 Combine like terms: -6.161137441 + 6.161137441 = 0.000000000 0.000000000 + -154.028436d + d2 = 0 + 6.161137441 -154.028436d + d2 = 0 + 6.161137441 Combine like terms: 0 + 6.161137441 = 6.161137441 -154.028436d + d2 = 6.161137441 The d term is -154.028436d. Take half its coefficient (-77.014218). Square it (5931.189774) and add it to both sides. Add '5931.189774' to each side of the equation. -154.028436d + 5931.189774 + d2 = 6.161137441 + 5931.189774 Reorder the terms: 5931.189774 + -154.028436d + d2 = 6.161137441 + 5931.189774 Combine like terms: 6.161137441 + 5931.189774 = 5937.350911441 5931.189774 + -154.028436d + d2 = 5937.350911441 Factor a perfect square on the left side: (d + -77.014218)(d + -77.014218) = 5937.350911441 Calculate the square root of the right side: 77.054207617 Break this problem into two subproblems by setting (d + -77.014218) equal to 77.054207617 and -77.054207617.Subproblem 1
d + -77.014218 = 77.054207617 Simplifying d + -77.014218 = 77.054207617 Reorder the terms: -77.014218 + d = 77.054207617 Solving -77.014218 + d = 77.054207617 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '77.014218' to each side of the equation. -77.014218 + 77.014218 + d = 77.054207617 + 77.014218 Combine like terms: -77.014218 + 77.014218 = 0.000000 0.000000 + d = 77.054207617 + 77.014218 d = 77.054207617 + 77.014218 Combine like terms: 77.054207617 + 77.014218 = 154.068425617 d = 154.068425617 Simplifying d = 154.068425617Subproblem 2
d + -77.014218 = -77.054207617 Simplifying d + -77.014218 = -77.054207617 Reorder the terms: -77.014218 + d = -77.054207617 Solving -77.014218 + d = -77.054207617 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '77.014218' to each side of the equation. -77.014218 + 77.014218 + d = -77.054207617 + 77.014218 Combine like terms: -77.014218 + 77.014218 = 0.000000 0.000000 + d = -77.054207617 + 77.014218 d = -77.054207617 + 77.014218 Combine like terms: -77.054207617 + 77.014218 = -0.039989617 d = -0.039989617 Simplifying d = -0.039989617Solution
The solution to the problem is based on the solutions from the subproblems. d = {154.068425617, -0.039989617}
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