1x+10x+25x(27-2x)=246

Solution for 1x+10x+25x(27-2x)=246 equation:

Simplifying
1x + 10x + 25x(27 + -2x) = 246
1x + 10x + (27 * 25x + -2x * 25x) = 246
1x + 10x + (675x + -50x2) = 246

Combine like terms: 1x + 10x = 11x
11x + 675x + -50x2 = 246

Combine like terms: 11x + 675x = 686x
686x + -50x2 = 246

Solving
686x + -50x2 = 246

Solving for variable 'x'.

Reorder the terms:
-246 + 686x + -50x2 = 246 + -246

Combine like terms: 246 + -246 = 0
-246 + 686x + -50x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-123 + 343x + -25x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-123 + 343x + -25x2)' equal to zero and attempt to solve:

Simplifying
-123 + 343x + -25x2 = 0

Solving
-123 + 343x + -25x2 = 0

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
4.92 + -13.72x + x2 = 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 + -4.92

Reorder the terms:
4.92 + -4.92 + -13.72x + x2 = 0 + -4.92

Combine like terms: 4.92 + -4.92 = 0.00
0.00 + -13.72x + x2 = 0 + -4.92
-13.72x + x2 = 0 + -4.92

Combine like terms: 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}
Solution
x = {13.351502137, 0.368497863}