0.1x^2+x=100

Solution for 0.1x^2+x=100 equation:

Simplifying
0.1x2 + x = 100

Reorder the terms:
x + 0.1x2 = 100

Solving
x + 0.1x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + x + 0.1x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + x + 0.1x2 = 0

Begin completing the square.  Divide all terms by
0.1 the coefficient of the squared term: 

Divide each side by '0.1'.
-1000 + 10x + x2 = 0

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 10x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 10x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 10x + x2 = 0 + 1000
10x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
10x + x2 = 1000

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
10x + 0.25 + x2 = 1000 + 0.25

Reorder the terms:
0.25 + 10x + x2 = 1000 + 0.25

Combine like terms: 1000 + 0.25 = 1000.25
0.25 + 10x + x2 = 1000.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1000.25

Calculate the square root of the right side: 31.626729202

Break this problem into two subproblems by setting 
(x + 0.5) equal to 31.626729202 and -31.626729202.

Subproblem 1
x + 0.5 = 31.626729202

Simplifying
x + 0.5 = 31.626729202

Reorder the terms:
0.5 + x = 31.626729202

Solving
0.5 + x = 31.626729202

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 31.626729202 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 31.626729202 + -0.5
x = 31.626729202 + -0.5

Combine like terms: 31.626729202 + -0.5 = 31.126729202
x = 31.126729202

Simplifying
x = 31.126729202

Subproblem 2
x + 0.5 = -31.626729202

Simplifying
x + 0.5 = -31.626729202

Reorder the terms:
0.5 + x = -31.626729202

Solving
0.5 + x = -31.626729202

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -31.626729202 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -31.626729202 + -0.5
x = -31.626729202 + -0.5

Combine like terms: -31.626729202 + -0.5 = -32.126729202
x = -32.126729202

Simplifying
x = -32.126729202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.126729202, -32.126729202}