x^2-6.5x+8=0

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Solution for x^2-6.5x+8=0 equation: 


Simplifying
x2 + -6.5x + 8 = 0

Reorder the terms:
8 + -6.5x + x2 = 0

Solving
8 + -6.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -6.5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -6.5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -6.5x + x2 = 0 + -8
-6.5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-6.5x + x2 = -8

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 = -8 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -8 + 10.5625

Combine like terms: -8 + 10.5625 = 2.5625
10.5625 + -6.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + -3.25) equal to 1.600781059 and -1.600781059.


Subproblem 1
x + -3.25 = 1.600781059

Simplifying
x + -3.25 = 1.600781059

Reorder the terms:
-3.25 + x = 1.600781059

Solving
-3.25 + x = 1.600781059

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 = 1.600781059 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 1.600781059 + 3.25
x = 1.600781059 + 3.25

Combine like terms: 1.600781059 + 3.25 = 4.850781059
x = 4.850781059

Simplifying
x = 4.850781059


Subproblem 2
x + -3.25 = -1.600781059

Simplifying
x + -3.25 = -1.600781059

Reorder the terms:
-3.25 + x = -1.600781059

Solving
-3.25 + x = -1.600781059

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 = -1.600781059 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -1.600781059 + 3.25
x = -1.600781059 + 3.25

Combine like terms: -1.600781059 + 3.25 = 1.649218941
x = 1.649218941

Simplifying
x = 1.649218941


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.850781059, 1.649218941}

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