25.32d^2-3900d-156=0

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Solution for 25.32d^2-3900d-156=0 equation: 


Simplifying
25.32d2 + -3900d + -156 = 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 = 154.068425617


Subproblem 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 = -0.039989617


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {154.068425617, -0.039989617}

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