10=0.013x^2-1.19x+28.24

Solution for 10=0.013x^2-1.19x+28.24 equation:

Simplifying
10 = 0.013x2 + -1.19x + 28.24

Reorder the terms:
10 = 28.24 + -1.19x + 0.013x2

Solving
10 = 28.24 + -1.19x + 0.013x2

Solving for variable 'x'.

Combine like terms: 10 + -28.24 = -18.24
-18.24 + 1.19x + -0.013x2 = 28.24 + -1.19x + 0.013x2 + -28.24 + 1.19x + -0.013x2

Reorder the terms:
-18.24 + 1.19x + -0.013x2 = 28.24 + -28.24 + -1.19x + 1.19x + 0.013x2 + -0.013x2

Combine like terms: 28.24 + -28.24 = 0.00
-18.24 + 1.19x + -0.013x2 = 0.00 + -1.19x + 1.19x + 0.013x2 + -0.013x2
-18.24 + 1.19x + -0.013x2 = -1.19x + 1.19x + 0.013x2 + -0.013x2

Combine like terms: -1.19x + 1.19x = 0.00
-18.24 + 1.19x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2
-18.24 + 1.19x + -0.013x2 = 0.013x2 + -0.013x2

Combine like terms: 0.013x2 + -0.013x2 = 0.000
-18.24 + 1.19x + -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'.
1403.076923 + -91.53846154x + x2 = 0

Move the constant term to the right:

Add '-1403.076923' to each side of the equation.
1403.076923 + -91.53846154x + -1403.076923 + x2 = 0 + -1403.076923

Reorder the terms:
1403.076923 + -1403.076923 + -91.53846154x + x2 = 0 + -1403.076923

Combine like terms: 1403.076923 + -1403.076923 = 0.000000
0.000000 + -91.53846154x + x2 = 0 + -1403.076923
-91.53846154x + x2 = 0 + -1403.076923

Combine like terms: 0 + -1403.076923 = -1403.076923
-91.53846154x + x2 = -1403.076923

The x term is -91.53846154x.  Take half its coefficient (-45.76923077).
Square it (2094.822485) and add it to both sides.

Add '2094.822485' to each side of the equation.
-91.53846154x + 2094.822485 + x2 = -1403.076923 + 2094.822485

Reorder the terms:
2094.822485 + -91.53846154x + x2 = -1403.076923 + 2094.822485

Combine like terms: -1403.076923 + 2094.822485 = 691.745562
2094.822485 + -91.53846154x + x2 = 691.745562

Factor a perfect square on the left side:
(x + -45.76923077)(x + -45.76923077) = 691.745562

Calculate the square root of the right side: 26.301056291

Break this problem into two subproblems by setting 
(x + -45.76923077) equal to 26.301056291 and -26.301056291.

Subproblem 1
x + -45.76923077 = 26.301056291

Simplifying
x + -45.76923077 = 26.301056291

Reorder the terms:
-45.76923077 + x = 26.301056291

Solving
-45.76923077 + x = 26.301056291

Solving for variable 'x'.

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

Add '45.76923077' to each side of the equation.
-45.76923077 + 45.76923077 + x = 26.301056291 + 45.76923077

Combine like terms: -45.76923077 + 45.76923077 = 0.00000000
0.00000000 + x = 26.301056291 + 45.76923077
x = 26.301056291 + 45.76923077

Combine like terms: 26.301056291 + 45.76923077 = 72.070287061
x = 72.070287061

Simplifying
x = 72.070287061

Subproblem 2
x + -45.76923077 = -26.301056291

Simplifying
x + -45.76923077 = -26.301056291

Reorder the terms:
-45.76923077 + x = -26.301056291

Solving
-45.76923077 + x = -26.301056291

Solving for variable 'x'.

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

Add '45.76923077' to each side of the equation.
-45.76923077 + 45.76923077 + x = -26.301056291 + 45.76923077

Combine like terms: -45.76923077 + 45.76923077 = 0.00000000
0.00000000 + x = -26.301056291 + 45.76923077
x = -26.301056291 + 45.76923077

Combine like terms: -26.301056291 + 45.76923077 = 19.468174479
x = 19.468174479

Simplifying
x = 19.468174479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {72.070287061, 19.468174479}