8x^2+8x-33=0

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


Simplifying
8x2 + 8x + -33 = 0

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

Solving
-33 + 8x + 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'.
-4.125 + x + x2 = 0

Move the constant term to the right:

Add '4.125' to each side of the equation.
-4.125 + x + 4.125 + x2 = 0 + 4.125

Reorder the terms:
-4.125 + 4.125 + x + x2 = 0 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + x + x2 = 0 + 4.125
x + x2 = 0 + 4.125

Combine like terms: 0 + 4.125 = 4.125
x + x2 = 4.125

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 4.125 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 4.125 + 0.25

Combine like terms: 4.125 + 0.25 = 4.375
1.25 + x2 = 4.375

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.375

Calculate the square root of the right side: 2.091650066

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.091650066 and -2.091650066.


Subproblem 1
x + 0.5 = 2.091650066

Simplifying
x + 0.5 = 2.091650066

Reorder the terms:
0.5 + x = 2.091650066

Solving
0.5 + x = 2.091650066

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.091650066 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.091650066 + -0.5
x = 2.091650066 + -0.5

Combine like terms: 2.091650066 + -0.5 = 1.591650066
x = 1.591650066

Simplifying
x = 1.591650066


Subproblem 2
x + 0.5 = -2.091650066

Simplifying
x + 0.5 = -2.091650066

Reorder the terms:
0.5 + x = -2.091650066

Solving
0.5 + x = -2.091650066

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.091650066 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.091650066 + -0.5
x = -2.091650066 + -0.5

Combine like terms: -2.091650066 + -0.5 = -2.591650066
x = -2.591650066

Simplifying
x = -2.591650066


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.591650066, -2.591650066}

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