20.22d^2-3900d-326=0

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Solution for 20.22d^2-3900d-326=0 equation: 


Simplifying
20.22d2 + -3900d + -326 = 0

Reorder the terms:
-326 + -3900d + 20.22d2 = 0

Solving
-326 + -3900d + 20.22d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
20.22 the coefficient of the squared term: 

Divide each side by '20.22'.
-16.12265084 + -192.8783383d + d2 = 0

Move the constant term to the right:

Add '16.12265084' to each side of the equation.
-16.12265084 + -192.8783383d + 16.12265084 + d2 = 0 + 16.12265084

Reorder the terms:
-16.12265084 + 16.12265084 + -192.8783383d + d2 = 0 + 16.12265084

Combine like terms: -16.12265084 + 16.12265084 = 0.00000000
0.00000000 + -192.8783383d + d2 = 0 + 16.12265084
-192.8783383d + d2 = 0 + 16.12265084

Combine like terms: 0 + 16.12265084 = 16.12265084
-192.8783383d + d2 = 16.12265084

The d term is -192.8783383d.  Take half its coefficient (-96.43916915).
Square it (9300.513346) and add it to both sides.

Add '9300.513346' to each side of the equation.
-192.8783383d + 9300.513346 + d2 = 16.12265084 + 9300.513346

Reorder the terms:
9300.513346 + -192.8783383d + d2 = 16.12265084 + 9300.513346

Combine like terms: 16.12265084 + 9300.513346 = 9316.63599684
9300.513346 + -192.8783383d + d2 = 9316.63599684

Factor a perfect square on the left side:
(d + -96.43916915)(d + -96.43916915) = 9316.63599684

Calculate the square root of the right side: 96.522722697

Break this problem into two subproblems by setting 
(d + -96.43916915) equal to 96.522722697 and -96.522722697.


Subproblem 1
d + -96.43916915 = 96.522722697

Simplifying
d + -96.43916915 = 96.522722697

Reorder the terms:
-96.43916915 + d = 96.522722697

Solving
-96.43916915 + d = 96.522722697

Solving for variable 'd'.

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

Add '96.43916915' to each side of the equation.
-96.43916915 + 96.43916915 + d = 96.522722697 + 96.43916915

Combine like terms: -96.43916915 + 96.43916915 = 0.00000000
0.00000000 + d = 96.522722697 + 96.43916915
d = 96.522722697 + 96.43916915

Combine like terms: 96.522722697 + 96.43916915 = 192.961891847
d = 192.961891847

Simplifying
d = 192.961891847


Subproblem 2
d + -96.43916915 = -96.522722697

Simplifying
d + -96.43916915 = -96.522722697

Reorder the terms:
-96.43916915 + d = -96.522722697

Solving
-96.43916915 + d = -96.522722697

Solving for variable 'd'.

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

Add '96.43916915' to each side of the equation.
-96.43916915 + 96.43916915 + d = -96.522722697 + 96.43916915

Combine like terms: -96.43916915 + 96.43916915 = 0.00000000
0.00000000 + d = -96.522722697 + 96.43916915
d = -96.522722697 + 96.43916915

Combine like terms: -96.522722697 + 96.43916915 = -0.083553547
d = -0.083553547

Simplifying
d = -0.083553547


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {192.961891847, -0.083553547}

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