x^2-5.5x-6=0

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Solution for x^2-5.5x-6=0 equation: 


Simplifying
x2 + -5.5x + -6 = 0

Reorder the terms:
-6 + -5.5x + x2 = 0

Solving
-6 + -5.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -5.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -5.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5.5x + x2 = 0 + 6
-5.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-5.5x + x2 = 6

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 = 6 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 6 + 7.5625

Combine like terms: 6 + 7.5625 = 13.5625
7.5625 + -5.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + -2.75) equal to 3.682729966 and -3.682729966.


Subproblem 1
x + -2.75 = 3.682729966

Simplifying
x + -2.75 = 3.682729966

Reorder the terms:
-2.75 + x = 3.682729966

Solving
-2.75 + x = 3.682729966

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 = 3.682729966 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 3.682729966 + 2.75
x = 3.682729966 + 2.75

Combine like terms: 3.682729966 + 2.75 = 6.432729966
x = 6.432729966

Simplifying
x = 6.432729966


Subproblem 2
x + -2.75 = -3.682729966

Simplifying
x + -2.75 = -3.682729966

Reorder the terms:
-2.75 + x = -3.682729966

Solving
-2.75 + x = -3.682729966

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 = -3.682729966 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -3.682729966 + 2.75
x = -3.682729966 + 2.75

Combine like terms: -3.682729966 + 2.75 = -0.932729966
x = -0.932729966

Simplifying
x = -0.932729966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.432729966, -0.932729966}

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