0.01x+0.10x+0.25x(27-2x)=2.46

Solution for 0.01x+0.10x+0.25x(27-2x)=2.46 equation:

Simplifying
0.01x + 0.10x + 0.25x(27 + -2x) = 2.46
0.01x + 0.10x + (27 * 0.25x + -2x * 0.25x) = 2.46
0.01x + 0.10x + (6.75x + -0.5x2) = 2.46

Combine like terms: 0.01x + 0.10x = 0.11x
0.11x + 6.75x + -0.5x2 = 2.46

Combine like terms: 0.11x + 6.75x = 6.86x
6.86x + -0.5x2 = 2.46

Solving
6.86x + -0.5x2 = 2.46

Solving for variable 'x'.

Reorder the terms:
-2.46 + 6.86x + -0.5x2 = 2.46 + -2.46

Combine like terms: 2.46 + -2.46 = 0.00
-2.46 + 6.86x + -0.5x2 = 0.00

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
4.92 + -13.72x + x2 = 0.0

Move the constant term to the right:

Add '-4.92' to each side of the equation.
4.92 + -13.72x + -4.92 + x2 = 0.0 + -4.92

Reorder the terms:
4.92 + -4.92 + -13.72x + x2 = 0.0 + -4.92

Combine like terms: 4.92 + -4.92 = 0.00
0.00 + -13.72x + x2 = 0.0 + -4.92
-13.72x + x2 = 0.0 + -4.92

Combine like terms: 0.0 + -4.92 = -4.92
-13.72x + x2 = -4.92

The x term is -13.72x.  Take half its coefficient (-6.86).
Square it (47.0596) and add it to both sides.

Add '47.0596' to each side of the equation.
-13.72x + 47.0596 + x2 = -4.92 + 47.0596

Reorder the terms:
47.0596 + -13.72x + x2 = -4.92 + 47.0596

Combine like terms: -4.92 + 47.0596 = 42.1396
47.0596 + -13.72x + x2 = 42.1396

Factor a perfect square on the left side:
(x + -6.86)(x + -6.86) = 42.1396

Calculate the square root of the right side: 6.491502137

Break this problem into two subproblems by setting 
(x + -6.86) equal to 6.491502137 and -6.491502137.

Subproblem 1
x + -6.86 = 6.491502137

Simplifying
x + -6.86 = 6.491502137

Reorder the terms:
-6.86 + x = 6.491502137

Solving
-6.86 + x = 6.491502137

Solving for variable 'x'.

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

Add '6.86' to each side of the equation.
-6.86 + 6.86 + x = 6.491502137 + 6.86

Combine like terms: -6.86 + 6.86 = 0.00
0.00 + x = 6.491502137 + 6.86
x = 6.491502137 + 6.86

Combine like terms: 6.491502137 + 6.86 = 13.351502137
x = 13.351502137

Simplifying
x = 13.351502137

Subproblem 2
x + -6.86 = -6.491502137

Simplifying
x + -6.86 = -6.491502137

Reorder the terms:
-6.86 + x = -6.491502137

Solving
-6.86 + x = -6.491502137

Solving for variable 'x'.

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

Add '6.86' to each side of the equation.
-6.86 + 6.86 + x = -6.491502137 + 6.86

Combine like terms: -6.86 + 6.86 = 0.00
0.00 + x = -6.491502137 + 6.86
x = -6.491502137 + 6.86

Combine like terms: -6.491502137 + 6.86 = 0.368497863
x = 0.368497863

Simplifying
x = 0.368497863

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.351502137, 0.368497863}