=100+30x+0.1x^2

Solution for =100+30x+0.1x^2 equation:

Simplifying
0 = 100 + 30x + 0.1x2

Solving
0 = 100 + 30x + 0.1x2

Solving for variable 'x'.

Combine like terms: 0 + -100 = -100
-100 + -30x + -0.1x2 = 100 + 30x + 0.1x2 + -100 + -30x + -0.1x2

Reorder the terms:
-100 + -30x + -0.1x2 = 100 + -100 + 30x + -30x + 0.1x2 + -0.1x2

Combine like terms: 100 + -100 = 0
-100 + -30x + -0.1x2 = 0 + 30x + -30x + 0.1x2 + -0.1x2
-100 + -30x + -0.1x2 = 30x + -30x + 0.1x2 + -0.1x2

Combine like terms: 30x + -30x = 0
-100 + -30x + -0.1x2 = 0 + 0.1x2 + -0.1x2
-100 + -30x + -0.1x2 = 0.1x2 + -0.1x2

Combine like terms: 0.1x2 + -0.1x2 = 0.0
-100 + -30x + -0.1x2 = 0.0

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

Divide each side by '-0.1'.
1000 + 300x + x2 = 0

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + 300x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + 300x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + 300x + x2 = 0 + -1000
300x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
300x + x2 = -1000

The x term is 300x.  Take half its coefficient (150).
Square it (22500) and add it to both sides.

Add '22500' to each side of the equation.
300x + 22500 + x2 = -1000 + 22500

Reorder the terms:
22500 + 300x + x2 = -1000 + 22500

Combine like terms: -1000 + 22500 = 21500
22500 + 300x + x2 = 21500

Factor a perfect square on the left side:
(x + 150)(x + 150) = 21500

Calculate the square root of the right side: 146.628782986

Break this problem into two subproblems by setting 
(x + 150) equal to 146.628782986 and -146.628782986.

Subproblem 1
x + 150 = 146.628782986

Simplifying
x + 150 = 146.628782986

Reorder the terms:
150 + x = 146.628782986

Solving
150 + x = 146.628782986

Solving for variable 'x'.

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

Add '-150' to each side of the equation.
150 + -150 + x = 146.628782986 + -150

Combine like terms: 150 + -150 = 0
0 + x = 146.628782986 + -150
x = 146.628782986 + -150

Combine like terms: 146.628782986 + -150 = -3.371217014
x = -3.371217014

Simplifying
x = -3.371217014

Subproblem 2
x + 150 = -146.628782986

Simplifying
x + 150 = -146.628782986

Reorder the terms:
150 + x = -146.628782986

Solving
150 + x = -146.628782986

Solving for variable 'x'.

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

Add '-150' to each side of the equation.
150 + -150 + x = -146.628782986 + -150

Combine like terms: 150 + -150 = 0
0 + x = -146.628782986 + -150
x = -146.628782986 + -150

Combine like terms: -146.628782986 + -150 = -296.628782986
x = -296.628782986

Simplifying
x = -296.628782986

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.371217014, -296.628782986}