x^2-5.2x+1=0

Solution for x^2-5.2x+1=0 equation:

Simplifying
x2 + -5.2x + 1 = 0

Reorder the terms:
1 + -5.2x + x2 = 0

Solving
1 + -5.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -5.2x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -5.2x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5.2x + x2 = 0 + -1
-5.2x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5.2x + x2 = -1

The x term is -5.2x.  Take half its coefficient (-2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
-5.2x + 6.76 + x2 = -1 + 6.76

Reorder the terms:
6.76 + -5.2x + x2 = -1 + 6.76

Combine like terms: -1 + 6.76 = 5.76
6.76 + -5.2x + x2 = 5.76

Factor a perfect square on the left side:
(x + -2.6)(x + -2.6) = 5.76

Calculate the square root of the right side: 2.4

Break this problem into two subproblems by setting 
(x + -2.6) equal to 2.4 and -2.4.

Subproblem 1
x + -2.6 = 2.4

Simplifying
x + -2.6 = 2.4

Reorder the terms:
-2.6 + x = 2.4

Solving
-2.6 + x = 2.4

Solving for variable 'x'.

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

Add '2.6' to each side of the equation.
-2.6 + 2.6 + x = 2.4 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + x = 2.4 + 2.6
x = 2.4 + 2.6

Combine like terms: 2.4 + 2.6 = 5
x = 5

Simplifying
x = 5

Subproblem 2
x + -2.6 = -2.4

Simplifying
x + -2.6 = -2.4

Reorder the terms:
-2.6 + x = -2.4

Solving
-2.6 + x = -2.4

Solving for variable 'x'.

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

Add '2.6' to each side of the equation.
-2.6 + 2.6 + x = -2.4 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + x = -2.4 + 2.6
x = -2.4 + 2.6

Combine like terms: -2.4 + 2.6 = 0.2
x = 0.2

Simplifying
x = 0.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, 0.2}