0.01x+0.10x+.25x(33-2x)=2.46

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Solution for 0.01x+0.10x+.25x(33-2x)=2.46 equation: 


Simplifying
0.01x + 0.10x + 0.25x(33 + -2x) = 2.46
0.01x + 0.10x + (33 * 0.25x + -2x * 0.25x) = 2.46
0.01x + 0.10x + (8.25x + -0.5x2) = 2.46

Combine like terms: 0.01x + 0.10x = 0.11x
0.11x + 8.25x + -0.5x2 = 2.46

Combine like terms: 0.11x + 8.25x = 8.36x
8.36x + -0.5x2 = 2.46

Solving
8.36x + -0.5x2 = 2.46

Solving for variable 'x'.

Reorder the terms:
-2.46 + 8.36x + -0.5x2 = 2.46 + -2.46

Combine like terms: 2.46 + -2.46 = 0.00
-2.46 + 8.36x + -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 + -16.72x + x2 = 0.0

Move the constant term to the right:

Add '-4.92' to each side of the equation.
4.92 + -16.72x + -4.92 + x2 = 0.0 + -4.92

Reorder the terms:
4.92 + -4.92 + -16.72x + x2 = 0.0 + -4.92

Combine like terms: 4.92 + -4.92 = 0.00
0.00 + -16.72x + x2 = 0.0 + -4.92
-16.72x + x2 = 0.0 + -4.92

Combine like terms: 0.0 + -4.92 = -4.92
-16.72x + x2 = -4.92

The x term is -16.72x.  Take half its coefficient (-8.36).
Square it (69.8896) and add it to both sides.

Add '69.8896' to each side of the equation.
-16.72x + 69.8896 + x2 = -4.92 + 69.8896

Reorder the terms:
69.8896 + -16.72x + x2 = -4.92 + 69.8896

Combine like terms: -4.92 + 69.8896 = 64.9696
69.8896 + -16.72x + x2 = 64.9696

Factor a perfect square on the left side:
(x + -8.36)(x + -8.36) = 64.9696

Calculate the square root of the right side: 8.0603722

Break this problem into two subproblems by setting 
(x + -8.36) equal to 8.0603722 and -8.0603722.


Subproblem 1
x + -8.36 = 8.0603722

Simplifying
x + -8.36 = 8.0603722

Reorder the terms:
-8.36 + x = 8.0603722

Solving
-8.36 + x = 8.0603722

Solving for variable 'x'.

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

Add '8.36' to each side of the equation.
-8.36 + 8.36 + x = 8.0603722 + 8.36

Combine like terms: -8.36 + 8.36 = 0.00
0.00 + x = 8.0603722 + 8.36
x = 8.0603722 + 8.36

Combine like terms: 8.0603722 + 8.36 = 16.4203722
x = 16.4203722

Simplifying
x = 16.4203722


Subproblem 2
x + -8.36 = -8.0603722

Simplifying
x + -8.36 = -8.0603722

Reorder the terms:
-8.36 + x = -8.0603722

Solving
-8.36 + x = -8.0603722

Solving for variable 'x'.

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

Add '8.36' to each side of the equation.
-8.36 + 8.36 + x = -8.0603722 + 8.36

Combine like terms: -8.36 + 8.36 = 0.00
0.00 + x = -8.0603722 + 8.36
x = -8.0603722 + 8.36

Combine like terms: -8.0603722 + 8.36 = 0.2996278
x = 0.2996278

Simplifying
x = 0.2996278


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.4203722, 0.2996278}

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