220.25-41x-x^2=0

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Solution for 220.25-41x-x^2=0 equation: 


Simplifying
220.25 + -41x + -1x2 = 0

Solving
220.25 + -41x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-220.25 + 41x + x2 = 0

Move the constant term to the right:

Add '220.25' to each side of the equation.
-220.25 + 41x + 220.25 + x2 = 0 + 220.25

Reorder the terms:
-220.25 + 220.25 + 41x + x2 = 0 + 220.25

Combine like terms: -220.25 + 220.25 = 0.00
0.00 + 41x + x2 = 0 + 220.25
41x + x2 = 0 + 220.25

Combine like terms: 0 + 220.25 = 220.25
41x + x2 = 220.25

The x term is 41x.  Take half its coefficient (20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
41x + 420.25 + x2 = 220.25 + 420.25

Reorder the terms:
420.25 + 41x + x2 = 220.25 + 420.25

Combine like terms: 220.25 + 420.25 = 640.5
420.25 + 41x + x2 = 640.5

Factor a perfect square on the left side:
(x + 20.5)(x + 20.5) = 640.5

Calculate the square root of the right side: 25.30810147

Break this problem into two subproblems by setting 
(x + 20.5) equal to 25.30810147 and -25.30810147.


Subproblem 1
x + 20.5 = 25.30810147

Simplifying
x + 20.5 = 25.30810147

Reorder the terms:
20.5 + x = 25.30810147

Solving
20.5 + x = 25.30810147

Solving for variable 'x'.

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

Add '-20.5' to each side of the equation.
20.5 + -20.5 + x = 25.30810147 + -20.5

Combine like terms: 20.5 + -20.5 = 0.0
0.0 + x = 25.30810147 + -20.5
x = 25.30810147 + -20.5

Combine like terms: 25.30810147 + -20.5 = 4.80810147
x = 4.80810147

Simplifying
x = 4.80810147


Subproblem 2
x + 20.5 = -25.30810147

Simplifying
x + 20.5 = -25.30810147

Reorder the terms:
20.5 + x = -25.30810147

Solving
20.5 + x = -25.30810147

Solving for variable 'x'.

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

Add '-20.5' to each side of the equation.
20.5 + -20.5 + x = -25.30810147 + -20.5

Combine like terms: 20.5 + -20.5 = 0.0
0.0 + x = -25.30810147 + -20.5
x = -25.30810147 + -20.5

Combine like terms: -25.30810147 + -20.5 = -45.80810147
x = -45.80810147

Simplifying
x = -45.80810147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.80810147, -45.80810147}

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