10x+x^2=1

Solution for 10x+x^2=1 equation:

Simplifying
10x + x2 = 1

Solving
10x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 10x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 10x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 10x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 10x + x2 = 0 + 1
10x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
10x + x2 = 1

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 = 1 + 25

Reorder the terms:
25 + 10x + x2 = 1 + 25

Combine like terms: 1 + 25 = 26
25 + 10x + x2 = 26

Factor a perfect square on the left side:
(x + 5)(x + 5) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 5) equal to 5.099019514 and -5.099019514.

Subproblem 1
x + 5 = 5.099019514

Simplifying
x + 5 = 5.099019514

Reorder the terms:
5 + x = 5.099019514

Solving
5 + x = 5.099019514

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 = 5.099019514 + -5

Combine like terms: 5 + -5 = 0
0 + x = 5.099019514 + -5
x = 5.099019514 + -5

Combine like terms: 5.099019514 + -5 = 0.099019514
x = 0.099019514

Simplifying
x = 0.099019514

Subproblem 2
x + 5 = -5.099019514

Simplifying
x + 5 = -5.099019514

Reorder the terms:
5 + x = -5.099019514

Solving
5 + x = -5.099019514

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 = -5.099019514 + -5

Combine like terms: 5 + -5 = 0
0 + x = -5.099019514 + -5
x = -5.099019514 + -5

Combine like terms: -5.099019514 + -5 = -10.099019514
x = -10.099019514

Simplifying
x = -10.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.099019514, -10.099019514}