5x^2+40x+8=0

Solution for 5x^2+40x+8=0 equation:

Simplifying
5x2 + 40x + 8 = 0

Reorder the terms:
8 + 40x + 5x2 = 0

Solving
8 + 40x + 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'.
1.6 + 8x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 8x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 8x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 8x + x2 = 0 + -1.6
8x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
8x + x2 = -1.6

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -1.6 + 16

Reorder the terms:
16 + 8x + x2 = -1.6 + 16

Combine like terms: -1.6 + 16 = 14.4
16 + 8x + x2 = 14.4

Factor a perfect square on the left side:
(x + 4)(x + 4) = 14.4

Calculate the square root of the right side: 3.794733192

Break this problem into two subproblems by setting 
(x + 4) equal to 3.794733192 and -3.794733192.

Subproblem 1
x + 4 = 3.794733192

Simplifying
x + 4 = 3.794733192

Reorder the terms:
4 + x = 3.794733192

Solving
4 + x = 3.794733192

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.794733192 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.794733192 + -4
x = 3.794733192 + -4

Combine like terms: 3.794733192 + -4 = -0.205266808
x = -0.205266808

Simplifying
x = -0.205266808

Subproblem 2
x + 4 = -3.794733192

Simplifying
x + 4 = -3.794733192

Reorder the terms:
4 + x = -3.794733192

Solving
4 + x = -3.794733192

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.794733192 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.794733192 + -4
x = -3.794733192 + -4

Combine like terms: -3.794733192 + -4 = -7.794733192
x = -7.794733192

Simplifying
x = -7.794733192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.205266808, -7.794733192}