8x^2+13x+4=0

Solution for 8x^2+13x+4=0 equation:

Simplifying
8x2 + 13x + 4 = 0

Reorder the terms:
4 + 13x + 8x2 = 0

Solving
4 + 13x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
0.5 + 1.625x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 1.625x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 1.625x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 1.625x + x2 = 0 + -0.5
1.625x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
1.625x + x2 = -0.5

The x term is 1.625x.  Take half its coefficient (0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
1.625x + 0.66015625 + x2 = -0.5 + 0.66015625

Reorder the terms:
0.66015625 + 1.625x + x2 = -0.5 + 0.66015625

Combine like terms: -0.5 + 0.66015625 = 0.16015625
0.66015625 + 1.625x + x2 = 0.16015625

Factor a perfect square on the left side:
(x + 0.8125)(x + 0.8125) = 0.16015625

Calculate the square root of the right side: 0.400195265

Break this problem into two subproblems by setting 
(x + 0.8125) equal to 0.400195265 and -0.400195265.

Subproblem 1
x + 0.8125 = 0.400195265

Simplifying
x + 0.8125 = 0.400195265

Reorder the terms:
0.8125 + x = 0.400195265

Solving
0.8125 + x = 0.400195265

Solving for variable 'x'.

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

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + x = 0.400195265 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + x = 0.400195265 + -0.8125
x = 0.400195265 + -0.8125

Combine like terms: 0.400195265 + -0.8125 = -0.412304735
x = -0.412304735

Simplifying
x = -0.412304735

Subproblem 2
x + 0.8125 = -0.400195265

Simplifying
x + 0.8125 = -0.400195265

Reorder the terms:
0.8125 + x = -0.400195265

Solving
0.8125 + x = -0.400195265

Solving for variable 'x'.

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

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + x = -0.400195265 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + x = -0.400195265 + -0.8125
x = -0.400195265 + -0.8125

Combine like terms: -0.400195265 + -0.8125 = -1.212695265
x = -1.212695265

Simplifying
x = -1.212695265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.412304735, -1.212695265}