4=0.013x^2-1.18x+28.24

Solution for 4=0.013x^2-1.18x+28.24 equation:

Simplifying
4 = 0.013x2 + -1.18x + 28.24

Reorder the terms:
4 = 28.24 + -1.18x + 0.013x2

Solving
4 = 28.24 + -1.18x + 0.013x2

Solving for variable 'x'.

Combine like terms: 4 + -28.24 = -24.24
-24.24 + 1.18x + -0.013x2 = 28.24 + -1.18x + 0.013x2 + -28.24 + 1.18x + -0.013x2

Reorder the terms:
-24.24 + 1.18x + -0.013x2 = 28.24 + -28.24 + -1.18x + 1.18x + 0.013x2 + -0.013x2

Combine like terms: 28.24 + -28.24 = 0.00
-24.24 + 1.18x + -0.013x2 = 0.00 + -1.18x + 1.18x + 0.013x2 + -0.013x2
-24.24 + 1.18x + -0.013x2 = -1.18x + 1.18x + 0.013x2 + -0.013x2

Combine like terms: -1.18x + 1.18x = 0.00
-24.24 + 1.18x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2
-24.24 + 1.18x + -0.013x2 = 0.013x2 + -0.013x2

Combine like terms: 0.013x2 + -0.013x2 = 0.000
-24.24 + 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'.
1864.615385 + -90.76923077x + x2 = 0

Move the constant term to the right:

Add '-1864.615385' to each side of the equation.
1864.615385 + -90.76923077x + -1864.615385 + x2 = 0 + -1864.615385

Reorder the terms:
1864.615385 + -1864.615385 + -90.76923077x + x2 = 0 + -1864.615385

Combine like terms: 1864.615385 + -1864.615385 = 0.000000
0.000000 + -90.76923077x + x2 = 0 + -1864.615385
-90.76923077x + x2 = 0 + -1864.615385

Combine like terms: 0 + -1864.615385 = -1864.615385
-90.76923077x + x2 = -1864.615385

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 = -1864.615385 + 2059.763314

Reorder the terms:
2059.763314 + -90.76923077x + x2 = -1864.615385 + 2059.763314

Combine like terms: -1864.615385 + 2059.763314 = 195.147929
2059.763314 + -90.76923077x + x2 = 195.147929

Factor a perfect square on the left side:
(x + -45.38461539)(x + -45.38461539) = 195.147929

Calculate the square root of the right side: 13.969535747

Break this problem into two subproblems by setting 
(x + -45.38461539) equal to 13.969535747 and -13.969535747.

Subproblem 1
x + -45.38461539 = 13.969535747

Simplifying
x + -45.38461539 = 13.969535747

Reorder the terms:
-45.38461539 + x = 13.969535747

Solving
-45.38461539 + x = 13.969535747

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 = 13.969535747 + 45.38461539

Combine like terms: -45.38461539 + 45.38461539 = 0.00000000
0.00000000 + x = 13.969535747 + 45.38461539
x = 13.969535747 + 45.38461539

Combine like terms: 13.969535747 + 45.38461539 = 59.354151137
x = 59.354151137

Simplifying
x = 59.354151137

Subproblem 2
x + -45.38461539 = -13.969535747

Simplifying
x + -45.38461539 = -13.969535747

Reorder the terms:
-45.38461539 + x = -13.969535747

Solving
-45.38461539 + x = -13.969535747

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 = -13.969535747 + 45.38461539

Combine like terms: -45.38461539 + 45.38461539 = 0.00000000
0.00000000 + x = -13.969535747 + 45.38461539
x = -13.969535747 + 45.38461539

Combine like terms: -13.969535747 + 45.38461539 = 31.415079643
x = 31.415079643

Simplifying
x = 31.415079643

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {59.354151137, 31.415079643}