x^2-6x-203=0

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Solution for x^2-6x-203=0 equation: 


Simplifying
x2 + -6x + -203 = 0

Reorder the terms:
-203 + -6x + x2 = 0

Solving
-203 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '203' to each side of the equation.
-203 + -6x + 203 + x2 = 0 + 203

Reorder the terms:
-203 + 203 + -6x + x2 = 0 + 203

Combine like terms: -203 + 203 = 0
0 + -6x + x2 = 0 + 203
-6x + x2 = 0 + 203

Combine like terms: 0 + 203 = 203
-6x + x2 = 203

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 203 + 9

Reorder the terms:
9 + -6x + x2 = 203 + 9

Combine like terms: 203 + 9 = 212
9 + -6x + x2 = 212

Factor a perfect square on the left side:
(x + -3)(x + -3) = 212

Calculate the square root of the right side: 14.560219779

Break this problem into two subproblems by setting 
(x + -3) equal to 14.560219779 and -14.560219779.


Subproblem 1
x + -3 = 14.560219779

Simplifying
x + -3 = 14.560219779

Reorder the terms:
-3 + x = 14.560219779

Solving
-3 + x = 14.560219779

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 14.560219779 + 3

Combine like terms: -3 + 3 = 0
0 + x = 14.560219779 + 3
x = 14.560219779 + 3

Combine like terms: 14.560219779 + 3 = 17.560219779
x = 17.560219779

Simplifying
x = 17.560219779


Subproblem 2
x + -3 = -14.560219779

Simplifying
x + -3 = -14.560219779

Reorder the terms:
-3 + x = -14.560219779

Solving
-3 + x = -14.560219779

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -14.560219779 + 3

Combine like terms: -3 + 3 = 0
0 + x = -14.560219779 + 3
x = -14.560219779 + 3

Combine like terms: -14.560219779 + 3 = -11.560219779
x = -11.560219779

Simplifying
x = -11.560219779


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.560219779, -11.560219779}

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