x^2+207362x-207359=0

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Solution for x^2+207362x-207359=0 equation: 


Simplifying
x2 + 207362x + -207359 = 0

Reorder the terms:
-207359 + 207362x + x2 = 0

Solving
-207359 + 207362x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '207359' to each side of the equation.
-207359 + 207362x + 207359 + x2 = 0 + 207359

Reorder the terms:
-207359 + 207359 + 207362x + x2 = 0 + 207359

Combine like terms: -207359 + 207359 = 0
0 + 207362x + x2 = 0 + 207359
207362x + x2 = 0 + 207359

Combine like terms: 0 + 207359 = 207359
207362x + x2 = 207359

The x term is 207362x.  Take half its coefficient (103681).
Square it (10749749760) and add it to both sides.

Add '10749749760' to each side of the equation.
207362x + 10749749760 + x2 = 207359 + 10749749760

Reorder the terms:
10749749760 + 207362x + x2 = 207359 + 10749749760

Combine like terms: 207359 + 10749749760 = 10749957119
10749749760 + 207362x + x2 = 10749957119

Factor a perfect square on the left side:
(x + 103681)(x + 103681) = 10749957119

Calculate the square root of the right side: 103681.999975888

Break this problem into two subproblems by setting 
(x + 103681) equal to 103681.999975888 and -103681.999975888.


Subproblem 1
x + 103681 = 103681.999975888

Simplifying
x + 103681 = 103681.999975888

Reorder the terms:
103681 + x = 103681.999975888

Solving
103681 + x = 103681.999975888

Solving for variable 'x'.

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

Add '-103681' to each side of the equation.
103681 + -103681 + x = 103681.999975888 + -103681

Combine like terms: 103681 + -103681 = 0
0 + x = 103681.999975888 + -103681
x = 103681.999975888 + -103681

Combine like terms: 103681.999975888 + -103681 = 0.999975888
x = 0.999975888

Simplifying
x = 0.999975888


Subproblem 2
x + 103681 = -103681.999975888

Simplifying
x + 103681 = -103681.999975888

Reorder the terms:
103681 + x = -103681.999975888

Solving
103681 + x = -103681.999975888

Solving for variable 'x'.

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

Add '-103681' to each side of the equation.
103681 + -103681 + x = -103681.999975888 + -103681

Combine like terms: 103681 + -103681 = 0
0 + x = -103681.999975888 + -103681
x = -103681.999975888 + -103681

Combine like terms: -103681.999975888 + -103681 = -207362.999975888
x = -207362.999975888

Simplifying
x = -207362.999975888


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.999975888, -207362.999975888}

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