x^2+22x+49=0

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Solution for x^2+22x+49=0 equation: 


Simplifying
x2 + 22x + 49 = 0

Reorder the terms:
49 + 22x + x2 = 0

Solving
49 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 22x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + 22x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 22x + x2 = 0 + -49
22x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
22x + x2 = -49

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 = -49 + 121

Reorder the terms:
121 + 22x + x2 = -49 + 121

Combine like terms: -49 + 121 = 72
121 + 22x + x2 = 72

Factor a perfect square on the left side:
(x + 11)(x + 11) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + 11) equal to 8.485281374 and -8.485281374.


Subproblem 1
x + 11 = 8.485281374

Simplifying
x + 11 = 8.485281374

Reorder the terms:
11 + x = 8.485281374

Solving
11 + x = 8.485281374

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 = 8.485281374 + -11

Combine like terms: 11 + -11 = 0
0 + x = 8.485281374 + -11
x = 8.485281374 + -11

Combine like terms: 8.485281374 + -11 = -2.514718626
x = -2.514718626

Simplifying
x = -2.514718626


Subproblem 2
x + 11 = -8.485281374

Simplifying
x + 11 = -8.485281374

Reorder the terms:
11 + x = -8.485281374

Solving
11 + x = -8.485281374

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 = -8.485281374 + -11

Combine like terms: 11 + -11 = 0
0 + x = -8.485281374 + -11
x = -8.485281374 + -11

Combine like terms: -8.485281374 + -11 = -19.485281374
x = -19.485281374

Simplifying
x = -19.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.514718626, -19.485281374}

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