0=1591.1791-80X+X^2

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Solution for 0=1591.1791-80X+X^2 equation: 


Simplifying
0 = 1591.1791 + -80X + X2

Solving
0 = 1591.1791 + -80X + X2

Solving for variable 'X'.

Combine like terms: 0 + -1591.1791 = -1591.1791
-1591.1791 + 80X + -1X2 = 1591.1791 + -80X + X2 + -1591.1791 + 80X + -1X2

Reorder the terms:
-1591.1791 + 80X + -1X2 = 1591.1791 + -1591.1791 + -80X + 80X + X2 + -1X2

Combine like terms: 1591.1791 + -1591.1791 = 0.0000
-1591.1791 + 80X + -1X2 = 0.0000 + -80X + 80X + X2 + -1X2
-1591.1791 + 80X + -1X2 = -80X + 80X + X2 + -1X2

Combine like terms: -80X + 80X = 0
-1591.1791 + 80X + -1X2 = 0 + X2 + -1X2
-1591.1791 + 80X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-1591.1791 + 80X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1591.1791 + -80X + X2 = 0

Move the constant term to the right:

Add '-1591.1791' to each side of the equation.
1591.1791 + -80X + -1591.1791 + X2 = 0 + -1591.1791

Reorder the terms:
1591.1791 + -1591.1791 + -80X + X2 = 0 + -1591.1791

Combine like terms: 1591.1791 + -1591.1791 = 0.0000
0.0000 + -80X + X2 = 0 + -1591.1791
-80X + X2 = 0 + -1591.1791

Combine like terms: 0 + -1591.1791 = -1591.1791
-80X + X2 = -1591.1791

The X term is -80X.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80X + 1600 + X2 = -1591.1791 + 1600

Reorder the terms:
1600 + -80X + X2 = -1591.1791 + 1600

Combine like terms: -1591.1791 + 1600 = 8.8209
1600 + -80X + X2 = 8.8209

Factor a perfect square on the left side:
(X + -40)(X + -40) = 8.8209

Calculate the square root of the right side: 2.97

Break this problem into two subproblems by setting 
(X + -40) equal to 2.97 and -2.97.


Subproblem 1
X + -40 = 2.97

Simplifying
X + -40 = 2.97

Reorder the terms:
-40 + X = 2.97

Solving
-40 + X = 2.97

Solving for variable 'X'.

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

Add '40' to each side of the equation.
-40 + 40 + X = 2.97 + 40

Combine like terms: -40 + 40 = 0
0 + X = 2.97 + 40
X = 2.97 + 40

Combine like terms: 2.97 + 40 = 42.97
X = 42.97

Simplifying
X = 42.97


Subproblem 2
X + -40 = -2.97

Simplifying
X + -40 = -2.97

Reorder the terms:
-40 + X = -2.97

Solving
-40 + X = -2.97

Solving for variable 'X'.

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

Add '40' to each side of the equation.
-40 + 40 + X = -2.97 + 40

Combine like terms: -40 + 40 = 0
0 + X = -2.97 + 40
X = -2.97 + 40

Combine like terms: -2.97 + 40 = 37.03
X = 37.03

Simplifying
X = 37.03


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {42.97, 37.03}

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