x^2-13x+4.47=0

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Solution for x^2-13x+4.47=0 equation: 


Simplifying
x2 + -13x + 4.47 = 0

Reorder the terms:
4.47 + -13x + x2 = 0

Solving
4.47 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4.47' to each side of the equation.
4.47 + -13x + -4.47 + x2 = 0 + -4.47

Reorder the terms:
4.47 + -4.47 + -13x + x2 = 0 + -4.47

Combine like terms: 4.47 + -4.47 = 0.00
0.00 + -13x + x2 = 0 + -4.47
-13x + x2 = 0 + -4.47

Combine like terms: 0 + -4.47 = -4.47
-13x + x2 = -4.47

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -4.47 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -4.47 + 42.25

Combine like terms: -4.47 + 42.25 = 37.78
42.25 + -13x + x2 = 37.78

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 37.78

Calculate the square root of the right side: 6.146543744

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.146543744 and -6.146543744.


Subproblem 1
x + -6.5 = 6.146543744

Simplifying
x + -6.5 = 6.146543744

Reorder the terms:
-6.5 + x = 6.146543744

Solving
-6.5 + x = 6.146543744

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 6.146543744 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 6.146543744 + 6.5
x = 6.146543744 + 6.5

Combine like terms: 6.146543744 + 6.5 = 12.646543744
x = 12.646543744

Simplifying
x = 12.646543744


Subproblem 2
x + -6.5 = -6.146543744

Simplifying
x + -6.5 = -6.146543744

Reorder the terms:
-6.5 + x = -6.146543744

Solving
-6.5 + x = -6.146543744

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -6.146543744 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -6.146543744 + 6.5
x = -6.146543744 + 6.5

Combine like terms: -6.146543744 + 6.5 = 0.353456256
x = 0.353456256

Simplifying
x = 0.353456256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.646543744, 0.353456256}

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