5x^2+33x-8=0

Solution for 5x^2+33x-8=0 equation:

Simplifying
5x2 + 33x + -8 = 0

Reorder the terms:
-8 + 33x + 5x2 = 0

Solving
-8 + 33x + 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 + 6.6x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 6.6x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 6.6x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 6.6x + x2 = 0 + 1.6
6.6x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
6.6x + x2 = 1.6

The x term is 6.6x.  Take half its coefficient (3.3).
Square it (10.89) and add it to both sides.

Add '10.89' to each side of the equation.
6.6x + 10.89 + x2 = 1.6 + 10.89

Reorder the terms:
10.89 + 6.6x + x2 = 1.6 + 10.89

Combine like terms: 1.6 + 10.89 = 12.49
10.89 + 6.6x + x2 = 12.49

Factor a perfect square on the left side:
(x + 3.3)(x + 3.3) = 12.49

Calculate the square root of the right side: 3.534119409

Break this problem into two subproblems by setting 
(x + 3.3) equal to 3.534119409 and -3.534119409.

Subproblem 1
x + 3.3 = 3.534119409

Simplifying
x + 3.3 = 3.534119409

Reorder the terms:
3.3 + x = 3.534119409

Solving
3.3 + x = 3.534119409

Solving for variable 'x'.

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

Add '-3.3' to each side of the equation.
3.3 + -3.3 + x = 3.534119409 + -3.3

Combine like terms: 3.3 + -3.3 = 0.0
0.0 + x = 3.534119409 + -3.3
x = 3.534119409 + -3.3

Combine like terms: 3.534119409 + -3.3 = 0.234119409
x = 0.234119409

Simplifying
x = 0.234119409

Subproblem 2
x + 3.3 = -3.534119409

Simplifying
x + 3.3 = -3.534119409

Reorder the terms:
3.3 + x = -3.534119409

Solving
3.3 + x = -3.534119409

Solving for variable 'x'.

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

Add '-3.3' to each side of the equation.
3.3 + -3.3 + x = -3.534119409 + -3.3

Combine like terms: 3.3 + -3.3 = 0.0
0.0 + x = -3.534119409 + -3.3
x = -3.534119409 + -3.3

Combine like terms: -3.534119409 + -3.3 = -6.834119409
x = -6.834119409

Simplifying
x = -6.834119409

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.234119409, -6.834119409}