5x^2+11x+1=0

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Solution for 5x^2+11x+1=0 equation:


Simplifying
5x2 + 11x + 1 = 0

Reorder the terms:
1 + 11x + 5x2 = 0

Solving
1 + 11x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.2 + 2.2x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2.2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2.2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2.2x + x2 = 0 + -0.2
2.2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2.2x + x2 = -0.2

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = -0.2 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = -0.2 + 1.21

Combine like terms: -0.2 + 1.21 = 1.01
1.21 + 2.2x + x2 = 1.01

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(x + 1.1) equal to 1.004987562 and -1.004987562.

Subproblem 1

x + 1.1 = 1.004987562 Simplifying x + 1.1 = 1.004987562 Reorder the terms: 1.1 + x = 1.004987562 Solving 1.1 + x = 1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.004987562 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.004987562 + -1.1 x = 1.004987562 + -1.1 Combine like terms: 1.004987562 + -1.1 = -0.095012438 x = -0.095012438 Simplifying x = -0.095012438

Subproblem 2

x + 1.1 = -1.004987562 Simplifying x + 1.1 = -1.004987562 Reorder the terms: 1.1 + x = -1.004987562 Solving 1.1 + x = -1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.004987562 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.004987562 + -1.1 x = -1.004987562 + -1.1 Combine like terms: -1.004987562 + -1.1 = -2.104987562 x = -2.104987562 Simplifying x = -2.104987562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.095012438, -2.104987562}

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