4x^2-9x-33=0

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Solution for 4x^2-9x-33=0 equation: 


Simplifying
4x2 + -9x + -33 = 0

Reorder the terms:
-33 + -9x + 4x2 = 0

Solving
-33 + -9x + 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 + -2.25x + x2 = 0

Move the constant term to the right:

Add '8.25' to each side of the equation.
-8.25 + -2.25x + 8.25 + x2 = 0 + 8.25

Reorder the terms:
-8.25 + 8.25 + -2.25x + x2 = 0 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + -2.25x + x2 = 0 + 8.25
-2.25x + x2 = 0 + 8.25

Combine like terms: 0 + 8.25 = 8.25
-2.25x + x2 = 8.25

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 8.25 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 8.25 + 1.265625

Combine like terms: 8.25 + 1.265625 = 9.515625
1.265625 + -2.25x + x2 = 9.515625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 9.515625

Calculate the square root of the right side: 3.08474067

Break this problem into two subproblems by setting 
(x + -1.125) equal to 3.08474067 and -3.08474067.


Subproblem 1
x + -1.125 = 3.08474067

Simplifying
x + -1.125 = 3.08474067

Reorder the terms:
-1.125 + x = 3.08474067

Solving
-1.125 + x = 3.08474067

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 3.08474067 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 3.08474067 + 1.125
x = 3.08474067 + 1.125

Combine like terms: 3.08474067 + 1.125 = 4.20974067
x = 4.20974067

Simplifying
x = 4.20974067


Subproblem 2
x + -1.125 = -3.08474067

Simplifying
x + -1.125 = -3.08474067

Reorder the terms:
-1.125 + x = -3.08474067

Solving
-1.125 + x = -3.08474067

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -3.08474067 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -3.08474067 + 1.125
x = -3.08474067 + 1.125

Combine like terms: -3.08474067 + 1.125 = -1.95974067
x = -1.95974067

Simplifying
x = -1.95974067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.20974067, -1.95974067}

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