250=.05(x*x)+1.1x

Solution for 250=.05(x*x)+1.1x equation:

Simplifying
250 = 0.05(x * x) + 1.1x

Multiply x * x
250 = 0.05(x2) + 1.1x

Reorder the terms:
250 = 1.1x + 0.05x2

Solving
250 = 1.1x + 0.05x2

Solving for variable 'x'.

Reorder the terms:
250 + -1.1x + -0.05x2 = 1.1x + -1.1x + 0.05x2 + -0.05x2

Combine like terms: 1.1x + -1.1x = 0.0
250 + -1.1x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2
250 + -1.1x + -0.05x2 = 0.05x2 + -0.05x2

Combine like terms: 0.05x2 + -0.05x2 = 0.00
250 + -1.1x + -0.05x2 = 0.00

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
-5000 + 22x + x2 = 0

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + 22x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + 22x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + 22x + x2 = 0 + 5000
22x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
22x + x2 = 5000

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 5000 + 121

Reorder the terms:
121 + 22x + x2 = 5000 + 121

Combine like terms: 5000 + 121 = 5121
121 + 22x + x2 = 5121

Factor a perfect square on the left side:
(x + 11)(x + 11) = 5121

Calculate the square root of the right side: 71.561162651

Break this problem into two subproblems by setting 
(x + 11) equal to 71.561162651 and -71.561162651.

Subproblem 1
x + 11 = 71.561162651

Simplifying
x + 11 = 71.561162651

Reorder the terms:
11 + x = 71.561162651

Solving
11 + x = 71.561162651

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 71.561162651 + -11

Combine like terms: 11 + -11 = 0
0 + x = 71.561162651 + -11
x = 71.561162651 + -11

Combine like terms: 71.561162651 + -11 = 60.561162651
x = 60.561162651

Simplifying
x = 60.561162651

Subproblem 2
x + 11 = -71.561162651

Simplifying
x + 11 = -71.561162651

Reorder the terms:
11 + x = -71.561162651

Solving
11 + x = -71.561162651

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -71.561162651 + -11

Combine like terms: 11 + -11 = 0
0 + x = -71.561162651 + -11
x = -71.561162651 + -11

Combine like terms: -71.561162651 + -11 = -82.561162651
x = -82.561162651

Simplifying
x = -82.561162651

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {60.561162651, -82.561162651}