x^2-5.5x+2.5=0

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Solution for x^2-5.5x+2.5=0 equation: 


Simplifying
x2 + -5.5x + 2.5 = 0

Reorder the terms:
2.5 + -5.5x + x2 = 0

Solving
2.5 + -5.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -5.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -5.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -5.5x + x2 = 0 + -2.5
-5.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-5.5x + x2 = -2.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -2.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -2.5 + 7.5625

Combine like terms: -2.5 + 7.5625 = 5.0625
7.5625 + -5.5x + x2 = 5.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.25 and -2.25.


Subproblem 1
x + -2.75 = 2.25

Simplifying
x + -2.75 = 2.25

Reorder the terms:
-2.75 + x = 2.25

Solving
-2.75 + x = 2.25

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 2.25 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.25 + 2.75
x = 2.25 + 2.75

Combine like terms: 2.25 + 2.75 = 5
x = 5

Simplifying
x = 5


Subproblem 2
x + -2.75 = -2.25

Simplifying
x + -2.75 = -2.25

Reorder the terms:
-2.75 + x = -2.25

Solving
-2.75 + x = -2.25

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -2.25 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.25 + 2.75
x = -2.25 + 2.75

Combine like terms: -2.25 + 2.75 = 0.5
x = 0.5

Simplifying
x = 0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, 0.5}

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