x^2-10x-199=0

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Solution for x^2-10x-199=0 equation: 


Simplifying
x2 + -10x + -199 = 0

Reorder the terms:
-199 + -10x + x2 = 0

Solving
-199 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '199' to each side of the equation.
-199 + -10x + 199 + x2 = 0 + 199

Reorder the terms:
-199 + 199 + -10x + x2 = 0 + 199

Combine like terms: -199 + 199 = 0
0 + -10x + x2 = 0 + 199
-10x + x2 = 0 + 199

Combine like terms: 0 + 199 = 199
-10x + x2 = 199

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 = 199 + 25

Reorder the terms:
25 + -10x + x2 = 199 + 25

Combine like terms: 199 + 25 = 224
25 + -10x + x2 = 224

Factor a perfect square on the left side:
(x + -5)(x + -5) = 224

Calculate the square root of the right side: 14.966629547

Break this problem into two subproblems by setting 
(x + -5) equal to 14.966629547 and -14.966629547.


Subproblem 1
x + -5 = 14.966629547

Simplifying
x + -5 = 14.966629547

Reorder the terms:
-5 + x = 14.966629547

Solving
-5 + x = 14.966629547

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 = 14.966629547 + 5

Combine like terms: -5 + 5 = 0
0 + x = 14.966629547 + 5
x = 14.966629547 + 5

Combine like terms: 14.966629547 + 5 = 19.966629547
x = 19.966629547

Simplifying
x = 19.966629547


Subproblem 2
x + -5 = -14.966629547

Simplifying
x + -5 = -14.966629547

Reorder the terms:
-5 + x = -14.966629547

Solving
-5 + x = -14.966629547

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 = -14.966629547 + 5

Combine like terms: -5 + 5 = 0
0 + x = -14.966629547 + 5
x = -14.966629547 + 5

Combine like terms: -14.966629547 + 5 = -9.966629547
x = -9.966629547

Simplifying
x = -9.966629547


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.966629547, -9.966629547}

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