x^2-5x+0.8=0

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Solution for x^2-5x+0.8=0 equation: 


Simplifying
x2 + -5x + 0.8 = 0

Reorder the terms:
0.8 + -5x + x2 = 0

Solving
0.8 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -5x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -5x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -5x + x2 = 0 + -0.8
-5x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-5x + x2 = -0.8

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -0.8 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -0.8 + 6.25

Combine like terms: -0.8 + 6.25 = 5.45
6.25 + -5x + x2 = 5.45

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5.45

Calculate the square root of the right side: 2.334523506

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.334523506 and -2.334523506.


Subproblem 1
x + -2.5 = 2.334523506

Simplifying
x + -2.5 = 2.334523506

Reorder the terms:
-2.5 + x = 2.334523506

Solving
-2.5 + x = 2.334523506

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.334523506 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.334523506 + 2.5
x = 2.334523506 + 2.5

Combine like terms: 2.334523506 + 2.5 = 4.834523506
x = 4.834523506

Simplifying
x = 4.834523506


Subproblem 2
x + -2.5 = -2.334523506

Simplifying
x + -2.5 = -2.334523506

Reorder the terms:
-2.5 + x = -2.334523506

Solving
-2.5 + x = -2.334523506

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.334523506 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.334523506 + 2.5
x = -2.334523506 + 2.5

Combine like terms: -2.334523506 + 2.5 = 0.165476494
x = 0.165476494

Simplifying
x = 0.165476494


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.834523506, 0.165476494}

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