x^2-10x-247=0

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Solution for x^2-10x-247=0 equation: 


Simplifying
x2 + -10x + -247 = 0

Reorder the terms:
-247 + -10x + x2 = 0

Solving
-247 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '247' to each side of the equation.
-247 + -10x + 247 + x2 = 0 + 247

Reorder the terms:
-247 + 247 + -10x + x2 = 0 + 247

Combine like terms: -247 + 247 = 0
0 + -10x + x2 = 0 + 247
-10x + x2 = 0 + 247

Combine like terms: 0 + 247 = 247
-10x + x2 = 247

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 = 247 + 25

Reorder the terms:
25 + -10x + x2 = 247 + 25

Combine like terms: 247 + 25 = 272
25 + -10x + x2 = 272

Factor a perfect square on the left side:
(x + -5)(x + -5) = 272

Calculate the square root of the right side: 16.492422502

Break this problem into two subproblems by setting 
(x + -5) equal to 16.492422502 and -16.492422502.


Subproblem 1
x + -5 = 16.492422502

Simplifying
x + -5 = 16.492422502

Reorder the terms:
-5 + x = 16.492422502

Solving
-5 + x = 16.492422502

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 = 16.492422502 + 5

Combine like terms: -5 + 5 = 0
0 + x = 16.492422502 + 5
x = 16.492422502 + 5

Combine like terms: 16.492422502 + 5 = 21.492422502
x = 21.492422502

Simplifying
x = 21.492422502


Subproblem 2
x + -5 = -16.492422502

Simplifying
x + -5 = -16.492422502

Reorder the terms:
-5 + x = -16.492422502

Solving
-5 + x = -16.492422502

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 = -16.492422502 + 5

Combine like terms: -5 + 5 = 0
0 + x = -16.492422502 + 5
x = -16.492422502 + 5

Combine like terms: -16.492422502 + 5 = -11.492422502
x = -11.492422502

Simplifying
x = -11.492422502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.492422502, -11.492422502}

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