33x^2+23x=5

Solution for 33x^2+23x=5 equation:

Simplifying
33x2 + 23x = 5

Reorder the terms:
23x + 33x2 = 5

Solving
23x + 33x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 23x + 33x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 23x + 33x2 = 0

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

Divide each side by '33'.
-0.1515151515 + 0.696969697x + x2 = 0

Move the constant term to the right:

Add '0.1515151515' to each side of the equation.
-0.1515151515 + 0.696969697x + 0.1515151515 + x2 = 0 + 0.1515151515

Reorder the terms:
-0.1515151515 + 0.1515151515 + 0.696969697x + x2 = 0 + 0.1515151515

Combine like terms: -0.1515151515 + 0.1515151515 = 0.0000000000
0.0000000000 + 0.696969697x + x2 = 0 + 0.1515151515
0.696969697x + x2 = 0 + 0.1515151515

Combine like terms: 0 + 0.1515151515 = 0.1515151515
0.696969697x + x2 = 0.1515151515

The x term is 0.696969697x.  Take half its coefficient (0.3484848485).
Square it (0.1214416896) and add it to both sides.

Add '0.1214416896' to each side of the equation.
0.696969697x + 0.1214416896 + x2 = 0.1515151515 + 0.1214416896

Reorder the terms:
0.1214416896 + 0.696969697x + x2 = 0.1515151515 + 0.1214416896

Combine like terms: 0.1515151515 + 0.1214416896 = 0.2729568411
0.1214416896 + 0.696969697x + x2 = 0.2729568411

Factor a perfect square on the left side:
(x + 0.3484848485)(x + 0.3484848485) = 0.2729568411

Calculate the square root of the right side: 0.522452717

Break this problem into two subproblems by setting 
(x + 0.3484848485) equal to 0.522452717 and -0.522452717.

Subproblem 1
x + 0.3484848485 = 0.522452717

Simplifying
x + 0.3484848485 = 0.522452717

Reorder the terms:
0.3484848485 + x = 0.522452717

Solving
0.3484848485 + x = 0.522452717

Solving for variable 'x'.

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

Add '-0.3484848485' to each side of the equation.
0.3484848485 + -0.3484848485 + x = 0.522452717 + -0.3484848485

Combine like terms: 0.3484848485 + -0.3484848485 = 0.0000000000
0.0000000000 + x = 0.522452717 + -0.3484848485
x = 0.522452717 + -0.3484848485

Combine like terms: 0.522452717 + -0.3484848485 = 0.1739678685
x = 0.1739678685

Simplifying
x = 0.1739678685

Subproblem 2
x + 0.3484848485 = -0.522452717

Simplifying
x + 0.3484848485 = -0.522452717

Reorder the terms:
0.3484848485 + x = -0.522452717

Solving
0.3484848485 + x = -0.522452717

Solving for variable 'x'.

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

Add '-0.3484848485' to each side of the equation.
0.3484848485 + -0.3484848485 + x = -0.522452717 + -0.3484848485

Combine like terms: 0.3484848485 + -0.3484848485 = 0.0000000000
0.0000000000 + x = -0.522452717 + -0.3484848485
x = -0.522452717 + -0.3484848485

Combine like terms: -0.522452717 + -0.3484848485 = -0.8709375655
x = -0.8709375655

Simplifying
x = -0.8709375655

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1739678685, -0.8709375655}