x^2+22x+65=0

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Solution for x^2+22x+65=0 equation: 


Simplifying
x2 + 22x + 65 = 0

Reorder the terms:
65 + 22x + x2 = 0

Solving
65 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-65' to each side of the equation.
65 + 22x + -65 + x2 = 0 + -65

Reorder the terms:
65 + -65 + 22x + x2 = 0 + -65

Combine like terms: 65 + -65 = 0
0 + 22x + x2 = 0 + -65
22x + x2 = 0 + -65

Combine like terms: 0 + -65 = -65
22x + x2 = -65

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -65 + 121

Reorder the terms:
121 + 22x + x2 = -65 + 121

Combine like terms: -65 + 121 = 56
121 + 22x + x2 = 56

Factor a perfect square on the left side:
(x + 11)(x + 11) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + 11) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + 11 = 7.483314774

Simplifying
x + 11 = 7.483314774

Reorder the terms:
11 + x = 7.483314774

Solving
11 + x = 7.483314774

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 7.483314774 + -11

Combine like terms: 11 + -11 = 0
0 + x = 7.483314774 + -11
x = 7.483314774 + -11

Combine like terms: 7.483314774 + -11 = -3.516685226
x = -3.516685226

Simplifying
x = -3.516685226


Subproblem 2
x + 11 = -7.483314774

Simplifying
x + 11 = -7.483314774

Reorder the terms:
11 + x = -7.483314774

Solving
11 + x = -7.483314774

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -7.483314774 + -11

Combine like terms: 11 + -11 = 0
0 + x = -7.483314774 + -11
x = -7.483314774 + -11

Combine like terms: -7.483314774 + -11 = -18.483314774
x = -18.483314774

Simplifying
x = -18.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.516685226, -18.483314774}

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