x^2-10x-208=0

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Solution for x^2-10x-208=0 equation: 


Simplifying
x2 + -10x + -208 = 0

Reorder the terms:
-208 + -10x + x2 = 0

Solving
-208 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '208' to each side of the equation.
-208 + -10x + 208 + x2 = 0 + 208

Reorder the terms:
-208 + 208 + -10x + x2 = 0 + 208

Combine like terms: -208 + 208 = 0
0 + -10x + x2 = 0 + 208
-10x + x2 = 0 + 208

Combine like terms: 0 + 208 = 208
-10x + x2 = 208

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 208 + 25

Reorder the terms:
25 + -10x + x2 = 208 + 25

Combine like terms: 208 + 25 = 233
25 + -10x + x2 = 233

Factor a perfect square on the left side:
(x + -5)(x + -5) = 233

Calculate the square root of the right side: 15.264337522

Break this problem into two subproblems by setting 
(x + -5) equal to 15.264337522 and -15.264337522.


Subproblem 1
x + -5 = 15.264337522

Simplifying
x + -5 = 15.264337522

Reorder the terms:
-5 + x = 15.264337522

Solving
-5 + x = 15.264337522

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 15.264337522 + 5

Combine like terms: -5 + 5 = 0
0 + x = 15.264337522 + 5
x = 15.264337522 + 5

Combine like terms: 15.264337522 + 5 = 20.264337522
x = 20.264337522

Simplifying
x = 20.264337522


Subproblem 2
x + -5 = -15.264337522

Simplifying
x + -5 = -15.264337522

Reorder the terms:
-5 + x = -15.264337522

Solving
-5 + x = -15.264337522

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -15.264337522 + 5

Combine like terms: -5 + 5 = 0
0 + x = -15.264337522 + 5
x = -15.264337522 + 5

Combine like terms: -15.264337522 + 5 = -10.264337522
x = -10.264337522

Simplifying
x = -10.264337522


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.264337522, -10.264337522}

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