4x^2-23x-33=0

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Solution for 4x^2-23x-33=0 equation: 


Simplifying
4x2 + -23x + -33 = 0

Reorder the terms:
-33 + -23x + 4x2 = 0

Solving
-33 + -23x + 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'.
-8.25 + -5.75x + x2 = 0

Move the constant term to the right:

Add '8.25' to each side of the equation.
-8.25 + -5.75x + 8.25 + x2 = 0 + 8.25

Reorder the terms:
-8.25 + 8.25 + -5.75x + x2 = 0 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + -5.75x + x2 = 0 + 8.25
-5.75x + x2 = 0 + 8.25

Combine like terms: 0 + 8.25 = 8.25
-5.75x + x2 = 8.25

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = 8.25 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = 8.25 + 8.265625

Combine like terms: 8.25 + 8.265625 = 16.515625
8.265625 + -5.75x + x2 = 16.515625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 16.515625

Calculate the square root of the right side: 4.063942052

Break this problem into two subproblems by setting 
(x + -2.875) equal to 4.063942052 and -4.063942052.


Subproblem 1
x + -2.875 = 4.063942052

Simplifying
x + -2.875 = 4.063942052

Reorder the terms:
-2.875 + x = 4.063942052

Solving
-2.875 + x = 4.063942052

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = 4.063942052 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = 4.063942052 + 2.875
x = 4.063942052 + 2.875

Combine like terms: 4.063942052 + 2.875 = 6.938942052
x = 6.938942052

Simplifying
x = 6.938942052


Subproblem 2
x + -2.875 = -4.063942052

Simplifying
x + -2.875 = -4.063942052

Reorder the terms:
-2.875 + x = -4.063942052

Solving
-2.875 + x = -4.063942052

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = -4.063942052 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = -4.063942052 + 2.875
x = -4.063942052 + 2.875

Combine like terms: -4.063942052 + 2.875 = -1.188942052
x = -1.188942052

Simplifying
x = -1.188942052


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.938942052, -1.188942052}

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