x^2+11x=-6

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Solution for x^2+11x=-6 equation:


Simplifying
x2 + 11x = -6

Reorder the terms:
11x + x2 = -6

Solving
11x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 11x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 11x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 11x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 11x + x2 = 0 + -6
11x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
11x + x2 = -6

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 = -6 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -6 + 30.25

Combine like terms: -6 + 30.25 = 24.25
30.25 + 11x + x2 = 24.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 5.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

x + 5.5 = 4.924428901 Simplifying x + 5.5 = 4.924428901 Reorder the terms: 5.5 + x = 4.924428901 Solving 5.5 + x = 4.924428901 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 = 4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.924428901 + -5.5 x = 4.924428901 + -5.5 Combine like terms: 4.924428901 + -5.5 = -0.575571099 x = -0.575571099 Simplifying x = -0.575571099

Subproblem 2

x + 5.5 = -4.924428901 Simplifying x + 5.5 = -4.924428901 Reorder the terms: 5.5 + x = -4.924428901 Solving 5.5 + x = -4.924428901 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 = -4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.924428901 + -5.5 x = -4.924428901 + -5.5 Combine like terms: -4.924428901 + -5.5 = -10.424428901 x = -10.424428901 Simplifying x = -10.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.575571099, -10.424428901}

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