2x^2+33x-8.5=0

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Solution for 2x^2+33x-8.5=0 equation: 


Simplifying
2x2 + 33x + -8.5 = 0

Reorder the terms:
-8.5 + 33x + 2x2 = 0

Solving
-8.5 + 33x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-4.25 + 16.5x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + 16.5x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + 16.5x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + 16.5x + x2 = 0 + 4.25
16.5x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
16.5x + x2 = 4.25

The x term is 16.5x.  Take half its coefficient (8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
16.5x + 68.0625 + x2 = 4.25 + 68.0625

Reorder the terms:
68.0625 + 16.5x + x2 = 4.25 + 68.0625

Combine like terms: 4.25 + 68.0625 = 72.3125
68.0625 + 16.5x + x2 = 72.3125

Factor a perfect square on the left side:
(x + 8.25)(x + 8.25) = 72.3125

Calculate the square root of the right side: 8.503675676

Break this problem into two subproblems by setting 
(x + 8.25) equal to 8.503675676 and -8.503675676.


Subproblem 1
x + 8.25 = 8.503675676

Simplifying
x + 8.25 = 8.503675676

Reorder the terms:
8.25 + x = 8.503675676

Solving
8.25 + x = 8.503675676

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = 8.503675676 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = 8.503675676 + -8.25
x = 8.503675676 + -8.25

Combine like terms: 8.503675676 + -8.25 = 0.253675676
x = 0.253675676

Simplifying
x = 0.253675676


Subproblem 2
x + 8.25 = -8.503675676

Simplifying
x + 8.25 = -8.503675676

Reorder the terms:
8.25 + x = -8.503675676

Solving
8.25 + x = -8.503675676

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = -8.503675676 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = -8.503675676 + -8.25
x = -8.503675676 + -8.25

Combine like terms: -8.503675676 + -8.25 = -16.753675676
x = -16.753675676

Simplifying
x = -16.753675676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.253675676, -16.753675676}

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