x^2+22x=-6

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Solution for x^2+22x=-6 equation:


Simplifying
x2 + 22x = -6

Reorder the terms:
22x + x2 = -6

Solving
22x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 22x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 22x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 22x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 22x + x2 = 0 + -6
22x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
22x + x2 = -6

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 = -6 + 121

Reorder the terms:
121 + 22x + x2 = -6 + 121

Combine like terms: -6 + 121 = 115
121 + 22x + x2 = 115

Factor a perfect square on the left side:
(x + 11)(x + 11) = 115

Calculate the square root of the right side: 10.723805295

Break this problem into two subproblems by setting 
(x + 11) equal to 10.723805295 and -10.723805295.

Subproblem 1

x + 11 = 10.723805295 Simplifying x + 11 = 10.723805295 Reorder the terms: 11 + x = 10.723805295 Solving 11 + x = 10.723805295 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 = 10.723805295 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.723805295 + -11 x = 10.723805295 + -11 Combine like terms: 10.723805295 + -11 = -0.276194705 x = -0.276194705 Simplifying x = -0.276194705

Subproblem 2

x + 11 = -10.723805295 Simplifying x + 11 = -10.723805295 Reorder the terms: 11 + x = -10.723805295 Solving 11 + x = -10.723805295 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 = -10.723805295 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.723805295 + -11 x = -10.723805295 + -11 Combine like terms: -10.723805295 + -11 = -21.723805295 x = -21.723805295 Simplifying x = -21.723805295

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.276194705, -21.723805295}

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