-.03x^2+8x-.41=0

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Solution for -.03x^2+8x-.41=0 equation: 


Simplifying
-0.03x2 + 8x + -0.41 = 0

Reorder the terms:
-0.41 + 8x + -0.03x2 = 0

Solving
-0.41 + 8x + -0.03x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.03 the coefficient of the squared term: 

Divide each side by '-0.03'.
13.66666667 + -266.6666667x + x2 = 0

Move the constant term to the right:

Add '-13.66666667' to each side of the equation.
13.66666667 + -266.6666667x + -13.66666667 + x2 = 0 + -13.66666667

Reorder the terms:
13.66666667 + -13.66666667 + -266.6666667x + x2 = 0 + -13.66666667

Combine like terms: 13.66666667 + -13.66666667 = 0.00000000
0.00000000 + -266.6666667x + x2 = 0 + -13.66666667
-266.6666667x + x2 = 0 + -13.66666667

Combine like terms: 0 + -13.66666667 = -13.66666667
-266.6666667x + x2 = -13.66666667

The x term is -266.6666667x.  Take half its coefficient (-133.3333334).
Square it (17777.77780) and add it to both sides.

Add '17777.77780' to each side of the equation.
-266.6666667x + 17777.77780 + x2 = -13.66666667 + 17777.77780

Reorder the terms:
17777.77780 + -266.6666667x + x2 = -13.66666667 + 17777.77780

Combine like terms: -13.66666667 + 17777.77780 = 17764.11113333
17777.77780 + -266.6666667x + x2 = 17764.11113333

Factor a perfect square on the left side:
(x + -133.3333334)(x + -133.3333334) = 17764.11113333

Calculate the square root of the right side: 133.282073563

Break this problem into two subproblems by setting 
(x + -133.3333334) equal to 133.282073563 and -133.282073563.


Subproblem 1
x + -133.3333334 = 133.282073563

Simplifying
x + -133.3333334 = 133.282073563

Reorder the terms:
-133.3333334 + x = 133.282073563

Solving
-133.3333334 + x = 133.282073563

Solving for variable 'x'.

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

Add '133.3333334' to each side of the equation.
-133.3333334 + 133.3333334 + x = 133.282073563 + 133.3333334

Combine like terms: -133.3333334 + 133.3333334 = 0.0000000
0.0000000 + x = 133.282073563 + 133.3333334
x = 133.282073563 + 133.3333334

Combine like terms: 133.282073563 + 133.3333334 = 266.615406963
x = 266.615406963

Simplifying
x = 266.615406963


Subproblem 2
x + -133.3333334 = -133.282073563

Simplifying
x + -133.3333334 = -133.282073563

Reorder the terms:
-133.3333334 + x = -133.282073563

Solving
-133.3333334 + x = -133.282073563

Solving for variable 'x'.

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

Add '133.3333334' to each side of the equation.
-133.3333334 + 133.3333334 + x = -133.282073563 + 133.3333334

Combine like terms: -133.3333334 + 133.3333334 = 0.0000000
0.0000000 + x = -133.282073563 + 133.3333334
x = -133.282073563 + 133.3333334

Combine like terms: -133.282073563 + 133.3333334 = 0.051259837
x = 0.051259837

Simplifying
x = 0.051259837


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {266.615406963, 0.051259837}

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