x^2-33x+213=0

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Solution for x^2-33x+213=0 equation: 


Simplifying
x2 + -33x + 213 = 0

Reorder the terms:
213 + -33x + x2 = 0

Solving
213 + -33x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-213' to each side of the equation.
213 + -33x + -213 + x2 = 0 + -213

Reorder the terms:
213 + -213 + -33x + x2 = 0 + -213

Combine like terms: 213 + -213 = 0
0 + -33x + x2 = 0 + -213
-33x + x2 = 0 + -213

Combine like terms: 0 + -213 = -213
-33x + x2 = -213

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 = -213 + 272.25

Reorder the terms:
272.25 + -33x + x2 = -213 + 272.25

Combine like terms: -213 + 272.25 = 59.25
272.25 + -33x + x2 = 59.25

Factor a perfect square on the left side:
(x + -16.5)(x + -16.5) = 59.25

Calculate the square root of the right side: 7.697402159

Break this problem into two subproblems by setting 
(x + -16.5) equal to 7.697402159 and -7.697402159.


Subproblem 1
x + -16.5 = 7.697402159

Simplifying
x + -16.5 = 7.697402159

Reorder the terms:
-16.5 + x = 7.697402159

Solving
-16.5 + x = 7.697402159

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 = 7.697402159 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = 7.697402159 + 16.5
x = 7.697402159 + 16.5

Combine like terms: 7.697402159 + 16.5 = 24.197402159
x = 24.197402159

Simplifying
x = 24.197402159


Subproblem 2
x + -16.5 = -7.697402159

Simplifying
x + -16.5 = -7.697402159

Reorder the terms:
-16.5 + x = -7.697402159

Solving
-16.5 + x = -7.697402159

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 = -7.697402159 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = -7.697402159 + 16.5
x = -7.697402159 + 16.5

Combine like terms: -7.697402159 + 16.5 = 8.802597841
x = 8.802597841

Simplifying
x = 8.802597841


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.197402159, 8.802597841}

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