x^2+11x+5=0

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Solution for x^2+11x+5=0 equation:


Simplifying
x2 + 11x + 5 = 0

Reorder the terms:
5 + 11x + x2 = 0

Solving
5 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 11x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 11x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 11x + x2 = 0 + -5
11x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
11x + x2 = -5

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 = -5 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -5 + 30.25

Combine like terms: -5 + 30.25 = 25.25
30.25 + 11x + x2 = 25.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.024937811 and -5.024937811.

Subproblem 1

x + 5.5 = 5.024937811 Simplifying x + 5.5 = 5.024937811 Reorder the terms: 5.5 + x = 5.024937811 Solving 5.5 + x = 5.024937811 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 = 5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.024937811 + -5.5 x = 5.024937811 + -5.5 Combine like terms: 5.024937811 + -5.5 = -0.475062189 x = -0.475062189 Simplifying x = -0.475062189

Subproblem 2

x + 5.5 = -5.024937811 Simplifying x + 5.5 = -5.024937811 Reorder the terms: 5.5 + x = -5.024937811 Solving 5.5 + x = -5.024937811 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 = -5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.024937811 + -5.5 x = -5.024937811 + -5.5 Combine like terms: -5.024937811 + -5.5 = -10.524937811 x = -10.524937811 Simplifying x = -10.524937811

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.475062189, -10.524937811}

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