x^2-80x+500=0

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Solution for x^2-80x+500=0 equation: 


Simplifying
x2 + -80x + 500 = 0

Reorder the terms:
500 + -80x + x2 = 0

Solving
500 + -80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-500' to each side of the equation.
500 + -80x + -500 + x2 = 0 + -500

Reorder the terms:
500 + -500 + -80x + x2 = 0 + -500

Combine like terms: 500 + -500 = 0
0 + -80x + x2 = 0 + -500
-80x + x2 = 0 + -500

Combine like terms: 0 + -500 = -500
-80x + x2 = -500

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 = -500 + 1600

Reorder the terms:
1600 + -80x + x2 = -500 + 1600

Combine like terms: -500 + 1600 = 1100
1600 + -80x + x2 = 1100

Factor a perfect square on the left side:
(x + -40)(x + -40) = 1100

Calculate the square root of the right side: 33.166247904

Break this problem into two subproblems by setting 
(x + -40) equal to 33.166247904 and -33.166247904.


Subproblem 1
x + -40 = 33.166247904

Simplifying
x + -40 = 33.166247904

Reorder the terms:
-40 + x = 33.166247904

Solving
-40 + x = 33.166247904

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 = 33.166247904 + 40

Combine like terms: -40 + 40 = 0
0 + x = 33.166247904 + 40
x = 33.166247904 + 40

Combine like terms: 33.166247904 + 40 = 73.166247904
x = 73.166247904

Simplifying
x = 73.166247904


Subproblem 2
x + -40 = -33.166247904

Simplifying
x + -40 = -33.166247904

Reorder the terms:
-40 + x = -33.166247904

Solving
-40 + x = -33.166247904

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 = -33.166247904 + 40

Combine like terms: -40 + 40 = 0
0 + x = -33.166247904 + 40
x = -33.166247904 + 40

Combine like terms: -33.166247904 + 40 = 6.833752096
x = 6.833752096

Simplifying
x = 6.833752096


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {73.166247904, 6.833752096}

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