.2x^2-80x+200=0

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Solution for .2x^2-80x+200=0 equation: 


Simplifying
0.2x2 + -80x + 200 = 0

Reorder the terms:
200 + -80x + 0.2x2 = 0

Solving
200 + -80x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
1000 + -400x + x2 = 0

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + -400x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + -400x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -400x + x2 = 0 + -1000
-400x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-400x + x2 = -1000

The x term is -400x.  Take half its coefficient (-200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
-400x + 40000 + x2 = -1000 + 40000

Reorder the terms:
40000 + -400x + x2 = -1000 + 40000

Combine like terms: -1000 + 40000 = 39000
40000 + -400x + x2 = 39000

Factor a perfect square on the left side:
(x + -200)(x + -200) = 39000

Calculate the square root of the right side: 197.484176581

Break this problem into two subproblems by setting 
(x + -200) equal to 197.484176581 and -197.484176581.


Subproblem 1
x + -200 = 197.484176581

Simplifying
x + -200 = 197.484176581

Reorder the terms:
-200 + x = 197.484176581

Solving
-200 + x = 197.484176581

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = 197.484176581 + 200

Combine like terms: -200 + 200 = 0
0 + x = 197.484176581 + 200
x = 197.484176581 + 200

Combine like terms: 197.484176581 + 200 = 397.484176581
x = 397.484176581

Simplifying
x = 397.484176581


Subproblem 2
x + -200 = -197.484176581

Simplifying
x + -200 = -197.484176581

Reorder the terms:
-200 + x = -197.484176581

Solving
-200 + x = -197.484176581

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = -197.484176581 + 200

Combine like terms: -200 + 200 = 0
0 + x = -197.484176581 + 200
x = -197.484176581 + 200

Combine like terms: -197.484176581 + 200 = 2.515823419
x = 2.515823419

Simplifying
x = 2.515823419


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {397.484176581, 2.515823419}

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