x^2+11x+2.75=0

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Solution for x^2+11x+2.75=0 equation:


Simplifying
x2 + 11x + 2.75 = 0

Reorder the terms:
2.75 + 11x + x2 = 0

Solving
2.75 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.75' to each side of the equation.
2.75 + 11x + -2.75 + x2 = 0 + -2.75

Reorder the terms:
2.75 + -2.75 + 11x + x2 = 0 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + 11x + x2 = 0 + -2.75
11x + x2 = 0 + -2.75

Combine like terms: 0 + -2.75 = -2.75
11x + x2 = -2.75

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -2.75 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -2.75 + 30.25

Combine like terms: -2.75 + 30.25 = 27.5
30.25 + 11x + x2 = 27.5

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 27.5

Calculate the square root of the right side: 5.244044241

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.244044241 and -5.244044241.


Subproblem 1
x + 5.5 = 5.244044241

Simplifying
x + 5.5 = 5.244044241

Reorder the terms:
5.5 + x = 5.244044241

Solving
5.5 + x = 5.244044241

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 5.244044241 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 5.244044241 + -5.5
x = 5.244044241 + -5.5

Combine like terms: 5.244044241 + -5.5 = -0.255955759
x = -0.255955759

Simplifying
x = -0.255955759


Subproblem 2
x + 5.5 = -5.244044241

Simplifying
x + 5.5 = -5.244044241

Reorder the terms:
5.5 + x = -5.244044241

Solving
5.5 + x = -5.244044241

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -5.244044241 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -5.244044241 + -5.5
x = -5.244044241 + -5.5

Combine like terms: -5.244044241 + -5.5 = -10.744044241
x = -10.744044241

Simplifying
x = -10.744044241


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.255955759, -10.744044241}

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