x^2+11x+9=0

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Solution for x^2+11x+9=0 equation:


Simplifying
x2 + 11x + 9 = 0

Reorder the terms:
9 + 11x + x2 = 0

Solving
9 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 11x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 11x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 11x + x2 = 0 + -9
11x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
11x + x2 = -9

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 = -9 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -9 + 30.25

Combine like terms: -9 + 30.25 = 21.25
30.25 + 11x + x2 = 21.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + 5.5) equal to 4.609772229 and -4.609772229.

Subproblem 1

x + 5.5 = 4.609772229 Simplifying x + 5.5 = 4.609772229 Reorder the terms: 5.5 + x = 4.609772229 Solving 5.5 + x = 4.609772229 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 = 4.609772229 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.609772229 + -5.5 x = 4.609772229 + -5.5 Combine like terms: 4.609772229 + -5.5 = -0.890227771 x = -0.890227771 Simplifying x = -0.890227771

Subproblem 2

x + 5.5 = -4.609772229 Simplifying x + 5.5 = -4.609772229 Reorder the terms: 5.5 + x = -4.609772229 Solving 5.5 + x = -4.609772229 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 = -4.609772229 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.609772229 + -5.5 x = -4.609772229 + -5.5 Combine like terms: -4.609772229 + -5.5 = -10.109772229 x = -10.109772229 Simplifying x = -10.109772229

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.890227771, -10.109772229}

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