x^2+11x+16=0

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Solution for x^2+11x+16=0 equation: 


Simplifying
x2 + 11x + 16 = 0

Reorder the terms:
16 + 11x + x2 = 0

Solving
16 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 11x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 11x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 11x + x2 = 0 + -16
11x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
11x + x2 = -16

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 = -16 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -16 + 30.25

Combine like terms: -16 + 30.25 = 14.25
30.25 + 11x + x2 = 14.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 5.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + 5.5 = 3.774917218

Simplifying
x + 5.5 = 3.774917218

Reorder the terms:
5.5 + x = 3.774917218

Solving
5.5 + x = 3.774917218

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 = 3.774917218 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 3.774917218 + -5.5
x = 3.774917218 + -5.5

Combine like terms: 3.774917218 + -5.5 = -1.725082782
x = -1.725082782

Simplifying
x = -1.725082782


Subproblem 2
x + 5.5 = -3.774917218

Simplifying
x + 5.5 = -3.774917218

Reorder the terms:
5.5 + x = -3.774917218

Solving
5.5 + x = -3.774917218

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 = -3.774917218 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -3.774917218 + -5.5
x = -3.774917218 + -5.5

Combine like terms: -3.774917218 + -5.5 = -9.274917218
x = -9.274917218

Simplifying
x = -9.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.725082782, -9.274917218}

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