3.91x-.00016x^2-3.79+2.39x=0

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Solution for 3.91x-.00016x^2-3.79+2.39x=0 equation: 


Simplifying
3.91x + -0.00016x2 + -3.79 + 2.39x = 0

Reorder the terms:
-3.79 + 3.91x + 2.39x + -0.00016x2 = 0

Combine like terms: 3.91x + 2.39x = 6.3x
-3.79 + 6.3x + -0.00016x2 = 0

Solving
-3.79 + 6.3x + -0.00016x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.00016 the coefficient of the squared term: 

Divide each side by '-0.00016'.
23687.5 + -39375x + x2 = 0

Move the constant term to the right:

Add '-23687.5' to each side of the equation.
23687.5 + -39375x + -23687.5 + x2 = 0 + -23687.5

Reorder the terms:
23687.5 + -23687.5 + -39375x + x2 = 0 + -23687.5

Combine like terms: 23687.5 + -23687.5 = 0.0
0.0 + -39375x + x2 = 0 + -23687.5
-39375x + x2 = 0 + -23687.5

Combine like terms: 0 + -23687.5 = -23687.5
-39375x + x2 = -23687.5

The x term is -39375x.  Take half its coefficient (-19687.5).
Square it (387597656.3) and add it to both sides.

Add '387597656.3' to each side of the equation.
-39375x + 387597656.3 + x2 = -23687.5 + 387597656.3

Reorder the terms:
387597656.3 + -39375x + x2 = -23687.5 + 387597656.3

Combine like terms: -23687.5 + 387597656.3 = 387573968.8
387597656.3 + -39375x + x2 = 387573968.8

Factor a perfect square on the left side:
(x + -19687.5)(x + -19687.5) = 387573968.8

Calculate the square root of the right side: 19686.898404777

Break this problem into two subproblems by setting 
(x + -19687.5) equal to 19686.898404777 and -19686.898404777.


Subproblem 1
x + -19687.5 = 19686.898404777

Simplifying
x + -19687.5 = 19686.898404777

Reorder the terms:
-19687.5 + x = 19686.898404777

Solving
-19687.5 + x = 19686.898404777

Solving for variable 'x'.

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

Add '19687.5' to each side of the equation.
-19687.5 + 19687.5 + x = 19686.898404777 + 19687.5

Combine like terms: -19687.5 + 19687.5 = 0.0
0.0 + x = 19686.898404777 + 19687.5
x = 19686.898404777 + 19687.5

Combine like terms: 19686.898404777 + 19687.5 = 39374.398404777
x = 39374.398404777

Simplifying
x = 39374.398404777


Subproblem 2
x + -19687.5 = -19686.898404777

Simplifying
x + -19687.5 = -19686.898404777

Reorder the terms:
-19687.5 + x = -19686.898404777

Solving
-19687.5 + x = -19686.898404777

Solving for variable 'x'.

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

Add '19687.5' to each side of the equation.
-19687.5 + 19687.5 + x = -19686.898404777 + 19687.5

Combine like terms: -19687.5 + 19687.5 = 0.0
0.0 + x = -19686.898404777 + 19687.5
x = -19686.898404777 + 19687.5

Combine like terms: -19686.898404777 + 19687.5 = 0.601595223
x = 0.601595223

Simplifying
x = 0.601595223


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {39374.398404777, 0.601595223}

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