5x^2+22x+7=0

Solution for 5x^2+22x+7=0 equation:

Simplifying
5x2 + 22x + 7 = 0

Reorder the terms:
7 + 22x + 5x2 = 0

Solving
7 + 22x + 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'.
1.4 + 4.4x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 4.4x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 4.4x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 4.4x + x2 = 0 + -1.4
4.4x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
4.4x + x2 = -1.4

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = -1.4 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = -1.4 + 4.84

Combine like terms: -1.4 + 4.84 = 3.44
4.84 + 4.4x + x2 = 3.44

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 3.44

Calculate the square root of the right side: 1.854723699

Break this problem into two subproblems by setting 
(x + 2.2) equal to 1.854723699 and -1.854723699.

Subproblem 1
x + 2.2 = 1.854723699

Simplifying
x + 2.2 = 1.854723699

Reorder the terms:
2.2 + x = 1.854723699

Solving
2.2 + x = 1.854723699

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = 1.854723699 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = 1.854723699 + -2.2
x = 1.854723699 + -2.2

Combine like terms: 1.854723699 + -2.2 = -0.345276301
x = -0.345276301

Simplifying
x = -0.345276301

Subproblem 2
x + 2.2 = -1.854723699

Simplifying
x + 2.2 = -1.854723699

Reorder the terms:
2.2 + x = -1.854723699

Solving
2.2 + x = -1.854723699

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = -1.854723699 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = -1.854723699 + -2.2
x = -1.854723699 + -2.2

Combine like terms: -1.854723699 + -2.2 = -4.054723699
x = -4.054723699

Simplifying
x = -4.054723699

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.345276301, -4.054723699}