4x^2+33x-8=0

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Solution for 4x^2+33x-8=0 equation: 


Simplifying
4x2 + 33x + -8 = 0

Reorder the terms:
-8 + 33x + 4x2 = 0

Solving
-8 + 33x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-2 + 8.25x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8.25x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 8.25x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8.25x + x2 = 0 + 2
8.25x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
8.25x + x2 = 2

The x term is 8.25x.  Take half its coefficient (4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
8.25x + 17.015625 + x2 = 2 + 17.015625

Reorder the terms:
17.015625 + 8.25x + x2 = 2 + 17.015625

Combine like terms: 2 + 17.015625 = 19.015625
17.015625 + 8.25x + x2 = 19.015625

Factor a perfect square on the left side:
(x + 4.125)(x + 4.125) = 19.015625

Calculate the square root of the right side: 4.360690886

Break this problem into two subproblems by setting 
(x + 4.125) equal to 4.360690886 and -4.360690886.


Subproblem 1
x + 4.125 = 4.360690886

Simplifying
x + 4.125 = 4.360690886

Reorder the terms:
4.125 + x = 4.360690886

Solving
4.125 + x = 4.360690886

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = 4.360690886 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = 4.360690886 + -4.125
x = 4.360690886 + -4.125

Combine like terms: 4.360690886 + -4.125 = 0.235690886
x = 0.235690886

Simplifying
x = 0.235690886


Subproblem 2
x + 4.125 = -4.360690886

Simplifying
x + 4.125 = -4.360690886

Reorder the terms:
4.125 + x = -4.360690886

Solving
4.125 + x = -4.360690886

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = -4.360690886 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = -4.360690886 + -4.125
x = -4.360690886 + -4.125

Combine like terms: -4.360690886 + -4.125 = -8.485690886
x = -8.485690886

Simplifying
x = -8.485690886


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.235690886, -8.485690886}

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