0.01x+0.10x+0.25x(26-2x)=1.82

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Solution for 0.01x+0.10x+0.25x(26-2x)=1.82 equation: 


Simplifying
0.01x + 0.10x + 0.25x(26 + -2x) = 1.82
0.01x + 0.10x + (26 * 0.25x + -2x * 0.25x) = 1.82
0.01x + 0.10x + (6.5x + -0.5x2) = 1.82

Combine like terms: 0.01x + 0.10x = 0.11x
0.11x + 6.5x + -0.5x2 = 1.82

Combine like terms: 0.11x + 6.5x = 6.61x
6.61x + -0.5x2 = 1.82

Solving
6.61x + -0.5x2 = 1.82

Solving for variable 'x'.

Reorder the terms:
-1.82 + 6.61x + -0.5x2 = 1.82 + -1.82

Combine like terms: 1.82 + -1.82 = 0.00
-1.82 + 6.61x + -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'.
3.64 + -13.22x + x2 = 0.0

Move the constant term to the right:

Add '-3.64' to each side of the equation.
3.64 + -13.22x + -3.64 + x2 = 0.0 + -3.64

Reorder the terms:
3.64 + -3.64 + -13.22x + x2 = 0.0 + -3.64

Combine like terms: 3.64 + -3.64 = 0.00
0.00 + -13.22x + x2 = 0.0 + -3.64
-13.22x + x2 = 0.0 + -3.64

Combine like terms: 0.0 + -3.64 = -3.64
-13.22x + x2 = -3.64

The x term is -13.22x.  Take half its coefficient (-6.61).
Square it (43.6921) and add it to both sides.

Add '43.6921' to each side of the equation.
-13.22x + 43.6921 + x2 = -3.64 + 43.6921

Reorder the terms:
43.6921 + -13.22x + x2 = -3.64 + 43.6921

Combine like terms: -3.64 + 43.6921 = 40.0521
43.6921 + -13.22x + x2 = 40.0521

Factor a perfect square on the left side:
(x + -6.61)(x + -6.61) = 40.0521

Calculate the square root of the right side: 6.328672847

Break this problem into two subproblems by setting 
(x + -6.61) equal to 6.328672847 and -6.328672847.


Subproblem 1
x + -6.61 = 6.328672847

Simplifying
x + -6.61 = 6.328672847

Reorder the terms:
-6.61 + x = 6.328672847

Solving
-6.61 + x = 6.328672847

Solving for variable 'x'.

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

Add '6.61' to each side of the equation.
-6.61 + 6.61 + x = 6.328672847 + 6.61

Combine like terms: -6.61 + 6.61 = 0.00
0.00 + x = 6.328672847 + 6.61
x = 6.328672847 + 6.61

Combine like terms: 6.328672847 + 6.61 = 12.938672847
x = 12.938672847

Simplifying
x = 12.938672847


Subproblem 2
x + -6.61 = -6.328672847

Simplifying
x + -6.61 = -6.328672847

Reorder the terms:
-6.61 + x = -6.328672847

Solving
-6.61 + x = -6.328672847

Solving for variable 'x'.

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

Add '6.61' to each side of the equation.
-6.61 + 6.61 + x = -6.328672847 + 6.61

Combine like terms: -6.61 + 6.61 = 0.00
0.00 + x = -6.328672847 + 6.61
x = -6.328672847 + 6.61

Combine like terms: -6.328672847 + 6.61 = 0.281327153
x = 0.281327153

Simplifying
x = 0.281327153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.938672847, 0.281327153}

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