x^2+22x+11=0

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Solution for x^2+22x+11=0 equation:


Simplifying
x2 + 22x + 11 = 0

Reorder the terms:
11 + 22x + x2 = 0

Solving
11 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 22x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 22x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 22x + x2 = 0 + -11
22x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
22x + x2 = -11

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 = -11 + 121

Reorder the terms:
121 + 22x + x2 = -11 + 121

Combine like terms: -11 + 121 = 110
121 + 22x + x2 = 110

Factor a perfect square on the left side:
(x + 11)(x + 11) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(x + 11) equal to 10.488088482 and -10.488088482.

Subproblem 1

x + 11 = 10.488088482 Simplifying x + 11 = 10.488088482 Reorder the terms: 11 + x = 10.488088482 Solving 11 + x = 10.488088482 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 = 10.488088482 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.488088482 + -11 x = 10.488088482 + -11 Combine like terms: 10.488088482 + -11 = -0.511911518 x = -0.511911518 Simplifying x = -0.511911518

Subproblem 2

x + 11 = -10.488088482 Simplifying x + 11 = -10.488088482 Reorder the terms: 11 + x = -10.488088482 Solving 11 + x = -10.488088482 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 = -10.488088482 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.488088482 + -11 x = -10.488088482 + -11 Combine like terms: -10.488088482 + -11 = -21.488088482 x = -21.488088482 Simplifying x = -21.488088482

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.511911518, -21.488088482}

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