.01815x+.0033x^2=5.5

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Solution for .01815x+.0033x^2=5.5 equation: 


Simplifying
0.01815x + 0.0033x2 = 5.5

Solving
0.01815x + 0.0033x2 = 5.5

Solving for variable 'x'.

Reorder the terms:
-5.5 + 0.01815x + 0.0033x2 = 5.5 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
-5.5 + 0.01815x + 0.0033x2 = 0.0

Begin completing the square.  Divide all terms by
0.0033 the coefficient of the squared term: 

Divide each side by '0.0033'.
-1666.666667 + 5.5x + x2 = 0

Move the constant term to the right:

Add '1666.666667' to each side of the equation.
-1666.666667 + 5.5x + 1666.666667 + x2 = 0 + 1666.666667

Reorder the terms:
-1666.666667 + 1666.666667 + 5.5x + x2 = 0 + 1666.666667

Combine like terms: -1666.666667 + 1666.666667 = 0.000000
0.000000 + 5.5x + x2 = 0 + 1666.666667
5.5x + x2 = 0 + 1666.666667

Combine like terms: 0 + 1666.666667 = 1666.666667
5.5x + x2 = 1666.666667

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 1666.666667 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 1666.666667 + 7.5625

Combine like terms: 1666.666667 + 7.5625 = 1674.229167
7.5625 + 5.5x + x2 = 1674.229167

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 1674.229167

Calculate the square root of the right side: 40.917345552

Break this problem into two subproblems by setting 
(x + 2.75) equal to 40.917345552 and -40.917345552.


Subproblem 1
x + 2.75 = 40.917345552

Simplifying
x + 2.75 = 40.917345552

Reorder the terms:
2.75 + x = 40.917345552

Solving
2.75 + x = 40.917345552

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 40.917345552 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 40.917345552 + -2.75
x = 40.917345552 + -2.75

Combine like terms: 40.917345552 + -2.75 = 38.167345552
x = 38.167345552

Simplifying
x = 38.167345552


Subproblem 2
x + 2.75 = -40.917345552

Simplifying
x + 2.75 = -40.917345552

Reorder the terms:
2.75 + x = -40.917345552

Solving
2.75 + x = -40.917345552

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -40.917345552 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -40.917345552 + -2.75
x = -40.917345552 + -2.75

Combine like terms: -40.917345552 + -2.75 = -43.667345552
x = -43.667345552

Simplifying
x = -43.667345552


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.167345552, -43.667345552}

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