d^2-17.825d-2721.623=0

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Solution for d^2-17.825d-2721.623=0 equation: 


Simplifying
d2 + -17.825d + -2721.623 = 0

Reorder the terms:
-2721.623 + -17.825d + d2 = 0

Solving
-2721.623 + -17.825d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '2721.623' to each side of the equation.
-2721.623 + -17.825d + 2721.623 + d2 = 0 + 2721.623

Reorder the terms:
-2721.623 + 2721.623 + -17.825d + d2 = 0 + 2721.623

Combine like terms: -2721.623 + 2721.623 = 0.000
0.000 + -17.825d + d2 = 0 + 2721.623
-17.825d + d2 = 0 + 2721.623

Combine like terms: 0 + 2721.623 = 2721.623
-17.825d + d2 = 2721.623

The d term is -17.825d.  Take half its coefficient (-8.9125).
Square it (79.43265625) and add it to both sides.

Add '79.43265625' to each side of the equation.
-17.825d + 79.43265625 + d2 = 2721.623 + 79.43265625

Reorder the terms:
79.43265625 + -17.825d + d2 = 2721.623 + 79.43265625

Combine like terms: 2721.623 + 79.43265625 = 2801.05565625
79.43265625 + -17.825d + d2 = 2801.05565625

Factor a perfect square on the left side:
(d + -8.9125)(d + -8.9125) = 2801.05565625

Calculate the square root of the right side: 52.925000295

Break this problem into two subproblems by setting 
(d + -8.9125) equal to 52.925000295 and -52.925000295.


Subproblem 1
d + -8.9125 = 52.925000295

Simplifying
d + -8.9125 = 52.925000295

Reorder the terms:
-8.9125 + d = 52.925000295

Solving
-8.9125 + d = 52.925000295

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '8.9125' to each side of the equation.
-8.9125 + 8.9125 + d = 52.925000295 + 8.9125

Combine like terms: -8.9125 + 8.9125 = 0.0000
0.0000 + d = 52.925000295 + 8.9125
d = 52.925000295 + 8.9125

Combine like terms: 52.925000295 + 8.9125 = 61.837500295
d = 61.837500295

Simplifying
d = 61.837500295


Subproblem 2
d + -8.9125 = -52.925000295

Simplifying
d + -8.9125 = -52.925000295

Reorder the terms:
-8.9125 + d = -52.925000295

Solving
-8.9125 + d = -52.925000295

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '8.9125' to each side of the equation.
-8.9125 + 8.9125 + d = -52.925000295 + 8.9125

Combine like terms: -8.9125 + 8.9125 = 0.0000
0.0000 + d = -52.925000295 + 8.9125
d = -52.925000295 + 8.9125

Combine like terms: -52.925000295 + 8.9125 = -44.012500295
d = -44.012500295

Simplifying
d = -44.012500295


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {61.837500295, -44.012500295}

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