4=.013x^2-1.18x+28.23

Solution for 4=.013x^2-1.18x+28.23 equation:

Simplifying
4 = 0.013x2 + -1.18x + 28.23

Reorder the terms:
4 = 28.23 + -1.18x + 0.013x2

Solving
4 = 28.23 + -1.18x + 0.013x2

Solving for variable 'x'.

Combine like terms: 4 + -28.23 = -24.23
-24.23 + 1.18x + -0.013x2 = 28.23 + -1.18x + 0.013x2 + -28.23 + 1.18x + -0.013x2

Reorder the terms:
-24.23 + 1.18x + -0.013x2 = 28.23 + -28.23 + -1.18x + 1.18x + 0.013x2 + -0.013x2

Combine like terms: 28.23 + -28.23 = 0.00
-24.23 + 1.18x + -0.013x2 = 0.00 + -1.18x + 1.18x + 0.013x2 + -0.013x2
-24.23 + 1.18x + -0.013x2 = -1.18x + 1.18x + 0.013x2 + -0.013x2

Combine like terms: -1.18x + 1.18x = 0.00
-24.23 + 1.18x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2
-24.23 + 1.18x + -0.013x2 = 0.013x2 + -0.013x2

Combine like terms: 0.013x2 + -0.013x2 = 0.000
-24.23 + 1.18x + -0.013x2 = 0.000

Begin completing the square.  Divide all terms by
-0.013 the coefficient of the squared term: 

Divide each side by '-0.013'.
1863.846154 + -90.76923077x + x2 = 0

Move the constant term to the right:

Add '-1863.846154' to each side of the equation.
1863.846154 + -90.76923077x + -1863.846154 + x2 = 0 + -1863.846154

Reorder the terms:
1863.846154 + -1863.846154 + -90.76923077x + x2 = 0 + -1863.846154

Combine like terms: 1863.846154 + -1863.846154 = 0.000000
0.000000 + -90.76923077x + x2 = 0 + -1863.846154
-90.76923077x + x2 = 0 + -1863.846154

Combine like terms: 0 + -1863.846154 = -1863.846154
-90.76923077x + x2 = -1863.846154

The x term is -90.76923077x.  Take half its coefficient (-45.38461539).
Square it (2059.763314) and add it to both sides.

Add '2059.763314' to each side of the equation.
-90.76923077x + 2059.763314 + x2 = -1863.846154 + 2059.763314

Reorder the terms:
2059.763314 + -90.76923077x + x2 = -1863.846154 + 2059.763314

Combine like terms: -1863.846154 + 2059.763314 = 195.91716
2059.763314 + -90.76923077x + x2 = 195.91716

Factor a perfect square on the left side:
(x + -45.38461539)(x + -45.38461539) = 195.91716

Calculate the square root of the right side: 13.997041116

Break this problem into two subproblems by setting 
(x + -45.38461539) equal to 13.997041116 and -13.997041116.

Subproblem 1
x + -45.38461539 = 13.997041116

Simplifying
x + -45.38461539 = 13.997041116

Reorder the terms:
-45.38461539 + x = 13.997041116

Solving
-45.38461539 + x = 13.997041116

Solving for variable 'x'.

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

Add '45.38461539' to each side of the equation.
-45.38461539 + 45.38461539 + x = 13.997041116 + 45.38461539

Combine like terms: -45.38461539 + 45.38461539 = 0.00000000
0.00000000 + x = 13.997041116 + 45.38461539
x = 13.997041116 + 45.38461539

Combine like terms: 13.997041116 + 45.38461539 = 59.381656506
x = 59.381656506

Simplifying
x = 59.381656506

Subproblem 2
x + -45.38461539 = -13.997041116

Simplifying
x + -45.38461539 = -13.997041116

Reorder the terms:
-45.38461539 + x = -13.997041116

Solving
-45.38461539 + x = -13.997041116

Solving for variable 'x'.

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

Add '45.38461539' to each side of the equation.
-45.38461539 + 45.38461539 + x = -13.997041116 + 45.38461539

Combine like terms: -45.38461539 + 45.38461539 = 0.00000000
0.00000000 + x = -13.997041116 + 45.38461539
x = -13.997041116 + 45.38461539

Combine like terms: -13.997041116 + 45.38461539 = 31.387574274
x = 31.387574274

Simplifying
x = 31.387574274

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {59.381656506, 31.387574274}