x^2-231x-21201=0

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Solution for x^2-231x-21201=0 equation: 


Simplifying
x2 + -231x + -21201 = 0

Reorder the terms:
-21201 + -231x + x2 = 0

Solving
-21201 + -231x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21201' to each side of the equation.
-21201 + -231x + 21201 + x2 = 0 + 21201

Reorder the terms:
-21201 + 21201 + -231x + x2 = 0 + 21201

Combine like terms: -21201 + 21201 = 0
0 + -231x + x2 = 0 + 21201
-231x + x2 = 0 + 21201

Combine like terms: 0 + 21201 = 21201
-231x + x2 = 21201

The x term is -231x.  Take half its coefficient (-115.5).
Square it (13340.25) and add it to both sides.

Add '13340.25' to each side of the equation.
-231x + 13340.25 + x2 = 21201 + 13340.25

Reorder the terms:
13340.25 + -231x + x2 = 21201 + 13340.25

Combine like terms: 21201 + 13340.25 = 34541.25
13340.25 + -231x + x2 = 34541.25

Factor a perfect square on the left side:
(x + -115.5)(x + -115.5) = 34541.25

Calculate the square root of the right side: 185.852764306

Break this problem into two subproblems by setting 
(x + -115.5) equal to 185.852764306 and -185.852764306.


Subproblem 1
x + -115.5 = 185.852764306

Simplifying
x + -115.5 = 185.852764306

Reorder the terms:
-115.5 + x = 185.852764306

Solving
-115.5 + x = 185.852764306

Solving for variable 'x'.

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

Add '115.5' to each side of the equation.
-115.5 + 115.5 + x = 185.852764306 + 115.5

Combine like terms: -115.5 + 115.5 = 0.0
0.0 + x = 185.852764306 + 115.5
x = 185.852764306 + 115.5

Combine like terms: 185.852764306 + 115.5 = 301.352764306
x = 301.352764306

Simplifying
x = 301.352764306


Subproblem 2
x + -115.5 = -185.852764306

Simplifying
x + -115.5 = -185.852764306

Reorder the terms:
-115.5 + x = -185.852764306

Solving
-115.5 + x = -185.852764306

Solving for variable 'x'.

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

Add '115.5' to each side of the equation.
-115.5 + 115.5 + x = -185.852764306 + 115.5

Combine like terms: -115.5 + 115.5 = 0.0
0.0 + x = -185.852764306 + 115.5
x = -185.852764306 + 115.5

Combine like terms: -185.852764306 + 115.5 = -70.352764306
x = -70.352764306

Simplifying
x = -70.352764306


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {301.352764306, -70.352764306}

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