10x+x^2=100

Solution for 10x+x^2=100 equation:

Simplifying
10x + x2 = 100

Solving
10x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 10x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 10x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 10x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 10x + x2 = 0 + 100
10x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
10x + x2 = 100

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 = 100 + 25

Reorder the terms:
25 + 10x + x2 = 100 + 25

Combine like terms: 100 + 25 = 125
25 + 10x + x2 = 125

Factor a perfect square on the left side:
(x + 5)(x + 5) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + 5) equal to 11.180339887 and -11.180339887.

Subproblem 1
x + 5 = 11.180339887

Simplifying
x + 5 = 11.180339887

Reorder the terms:
5 + x = 11.180339887

Solving
5 + x = 11.180339887

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 = 11.180339887 + -5

Combine like terms: 5 + -5 = 0
0 + x = 11.180339887 + -5
x = 11.180339887 + -5

Combine like terms: 11.180339887 + -5 = 6.180339887
x = 6.180339887

Simplifying
x = 6.180339887

Subproblem 2
x + 5 = -11.180339887

Simplifying
x + 5 = -11.180339887

Reorder the terms:
5 + x = -11.180339887

Solving
5 + x = -11.180339887

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 = -11.180339887 + -5

Combine like terms: 5 + -5 = 0
0 + x = -11.180339887 + -5
x = -11.180339887 + -5

Combine like terms: -11.180339887 + -5 = -16.180339887
x = -16.180339887

Simplifying
x = -16.180339887

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.180339887, -16.180339887}