x^2-6.5x+6.5=0

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Solution for x^2-6.5x+6.5=0 equation: 


Simplifying
x2 + -6.5x + 6.5 = 0

Reorder the terms:
6.5 + -6.5x + x2 = 0

Solving
6.5 + -6.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -6.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -6.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -6.5x + x2 = 0 + -6.5
-6.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-6.5x + x2 = -6.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -6.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -6.5 + 10.5625

Combine like terms: -6.5 + 10.5625 = 4.0625
10.5625 + -6.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + -3.25) equal to 2.015564437 and -2.015564437.


Subproblem 1
x + -3.25 = 2.015564437

Simplifying
x + -3.25 = 2.015564437

Reorder the terms:
-3.25 + x = 2.015564437

Solving
-3.25 + x = 2.015564437

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 2.015564437 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 2.015564437 + 3.25
x = 2.015564437 + 3.25

Combine like terms: 2.015564437 + 3.25 = 5.265564437
x = 5.265564437

Simplifying
x = 5.265564437


Subproblem 2
x + -3.25 = -2.015564437

Simplifying
x + -3.25 = -2.015564437

Reorder the terms:
-3.25 + x = -2.015564437

Solving
-3.25 + x = -2.015564437

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -2.015564437 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -2.015564437 + 3.25
x = -2.015564437 + 3.25

Combine like terms: -2.015564437 + 3.25 = 1.234435563
x = 1.234435563

Simplifying
x = 1.234435563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.265564437, 1.234435563}

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