x^2-4x-33=0

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


Simplifying
x2 + -4x + -33 = 0

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

Solving
-33 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -4x + 33 + x2 = 0 + 33

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

Combine like terms: -33 + 33 = 0
0 + -4x + x2 = 0 + 33
-4x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-4x + x2 = 33

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 33 + 4

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

Combine like terms: 33 + 4 = 37
4 + -4x + x2 = 37

Factor a perfect square on the left side:
(x + -2)(x + -2) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -2) equal to 6.08276253 and -6.08276253.


Subproblem 1
x + -2 = 6.08276253

Simplifying
x + -2 = 6.08276253

Reorder the terms:
-2 + x = 6.08276253

Solving
-2 + x = 6.08276253

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 6.08276253 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.08276253 + 2
x = 6.08276253 + 2

Combine like terms: 6.08276253 + 2 = 8.08276253
x = 8.08276253

Simplifying
x = 8.08276253


Subproblem 2
x + -2 = -6.08276253

Simplifying
x + -2 = -6.08276253

Reorder the terms:
-2 + x = -6.08276253

Solving
-2 + x = -6.08276253

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -6.08276253 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.08276253 + 2
x = -6.08276253 + 2

Combine like terms: -6.08276253 + 2 = -4.08276253
x = -4.08276253

Simplifying
x = -4.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.08276253, -4.08276253}

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