x^2-33x-16=0

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Solution for x^2-33x-16=0 equation: 


Simplifying
x2 + -33x + -16 = 0

Reorder the terms:
-16 + -33x + x2 = 0

Solving
-16 + -33x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -33x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -33x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -33x + x2 = 0 + 16
-33x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-33x + x2 = 16

The x term is -33x.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33x + 272.25 + x2 = 16 + 272.25

Reorder the terms:
272.25 + -33x + x2 = 16 + 272.25

Combine like terms: 16 + 272.25 = 288.25
272.25 + -33x + x2 = 288.25

Factor a perfect square on the left side:
(x + -16.5)(x + -16.5) = 288.25

Calculate the square root of the right side: 16.977926846

Break this problem into two subproblems by setting 
(x + -16.5) equal to 16.977926846 and -16.977926846.


Subproblem 1
x + -16.5 = 16.977926846

Simplifying
x + -16.5 = 16.977926846

Reorder the terms:
-16.5 + x = 16.977926846

Solving
-16.5 + x = 16.977926846

Solving for variable 'x'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x = 16.977926846 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = 16.977926846 + 16.5
x = 16.977926846 + 16.5

Combine like terms: 16.977926846 + 16.5 = 33.477926846
x = 33.477926846

Simplifying
x = 33.477926846


Subproblem 2
x + -16.5 = -16.977926846

Simplifying
x + -16.5 = -16.977926846

Reorder the terms:
-16.5 + x = -16.977926846

Solving
-16.5 + x = -16.977926846

Solving for variable 'x'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x = -16.977926846 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = -16.977926846 + 16.5
x = -16.977926846 + 16.5

Combine like terms: -16.977926846 + 16.5 = -0.477926846
x = -0.477926846

Simplifying
x = -0.477926846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.477926846, -0.477926846}

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