x^2-9x+5.5=0

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Solution for x^2-9x+5.5=0 equation: 


Simplifying
x2 + -9x + 5.5 = 0

Reorder the terms:
5.5 + -9x + x2 = 0

Solving
5.5 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -9x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -9x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -9x + x2 = 0 + -5.5
-9x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-9x + x2 = -5.5

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -5.5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -5.5 + 20.25

Combine like terms: -5.5 + 20.25 = 14.75
20.25 + -9x + x2 = 14.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 14.75

Calculate the square root of the right side: 3.840572874

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.840572874 and -3.840572874.


Subproblem 1
x + -4.5 = 3.840572874

Simplifying
x + -4.5 = 3.840572874

Reorder the terms:
-4.5 + x = 3.840572874

Solving
-4.5 + x = 3.840572874

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.840572874 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.840572874 + 4.5
x = 3.840572874 + 4.5

Combine like terms: 3.840572874 + 4.5 = 8.340572874
x = 8.340572874

Simplifying
x = 8.340572874


Subproblem 2
x + -4.5 = -3.840572874

Simplifying
x + -4.5 = -3.840572874

Reorder the terms:
-4.5 + x = -3.840572874

Solving
-4.5 + x = -3.840572874

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.840572874 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.840572874 + 4.5
x = -3.840572874 + 4.5

Combine like terms: -3.840572874 + 4.5 = 0.659427126
x = 0.659427126

Simplifying
x = 0.659427126


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.340572874, 0.659427126}

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