# 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 1x + 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 2x + 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

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