x^2-5.5*x-7.3=0

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Solution for x^2-5.5*x-7.3=0 equation: 


Simplifying
x2 + -5.5x + -7.3 = 0

Reorder the terms:
-7.3 + -5.5x + x2 = 0

Solving
-7.3 + -5.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7.3' to each side of the equation.
-7.3 + -5.5x + 7.3 + x2 = 0 + 7.3

Reorder the terms:
-7.3 + 7.3 + -5.5x + x2 = 0 + 7.3

Combine like terms: -7.3 + 7.3 = 0.0
0.0 + -5.5x + x2 = 0 + 7.3
-5.5x + x2 = 0 + 7.3

Combine like terms: 0 + 7.3 = 7.3
-5.5x + x2 = 7.3

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 = 7.3 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 7.3 + 7.5625

Combine like terms: 7.3 + 7.5625 = 14.8625
7.5625 + -5.5x + x2 = 14.8625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 14.8625

Calculate the square root of the right side: 3.855191305

Break this problem into two subproblems by setting 
(x + -2.75) equal to 3.855191305 and -3.855191305.


Subproblem 1
x + -2.75 = 3.855191305

Simplifying
x + -2.75 = 3.855191305

Reorder the terms:
-2.75 + x = 3.855191305

Solving
-2.75 + x = 3.855191305

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 = 3.855191305 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 3.855191305 + 2.75
x = 3.855191305 + 2.75

Combine like terms: 3.855191305 + 2.75 = 6.605191305
x = 6.605191305

Simplifying
x = 6.605191305


Subproblem 2
x + -2.75 = -3.855191305

Simplifying
x + -2.75 = -3.855191305

Reorder the terms:
-2.75 + x = -3.855191305

Solving
-2.75 + x = -3.855191305

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 = -3.855191305 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -3.855191305 + 2.75
x = -3.855191305 + 2.75

Combine like terms: -3.855191305 + 2.75 = -1.105191305
x = -1.105191305

Simplifying
x = -1.105191305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.605191305, -1.105191305}

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