x^2-5x+6.05=0

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Solution for x^2-5x+6.05=0 equation: 


Simplifying
x2 + -5x + 6.05 = 0

Reorder the terms:
6.05 + -5x + x2 = 0

Solving
6.05 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6.05' to each side of the equation.
6.05 + -5x + -6.05 + x2 = 0 + -6.05

Reorder the terms:
6.05 + -6.05 + -5x + x2 = 0 + -6.05

Combine like terms: 6.05 + -6.05 = 0.00
0.00 + -5x + x2 = 0 + -6.05
-5x + x2 = 0 + -6.05

Combine like terms: 0 + -6.05 = -6.05
-5x + x2 = -6.05

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 = -6.05 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -6.05 + 6.25

Combine like terms: -6.05 + 6.25 = 0.2
6.25 + -5x + x2 = 0.2

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.447213596 and -0.447213596.


Subproblem 1
x + -2.5 = 0.447213596

Simplifying
x + -2.5 = 0.447213596

Reorder the terms:
-2.5 + x = 0.447213596

Solving
-2.5 + x = 0.447213596

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 = 0.447213596 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0.447213596 + 2.5
x = 0.447213596 + 2.5

Combine like terms: 0.447213596 + 2.5 = 2.947213596
x = 2.947213596

Simplifying
x = 2.947213596


Subproblem 2
x + -2.5 = -0.447213596

Simplifying
x + -2.5 = -0.447213596

Reorder the terms:
-2.5 + x = -0.447213596

Solving
-2.5 + x = -0.447213596

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 = -0.447213596 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -0.447213596 + 2.5
x = -0.447213596 + 2.5

Combine like terms: -0.447213596 + 2.5 = 2.052786404
x = 2.052786404

Simplifying
x = 2.052786404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.947213596, 2.052786404}

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