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 = 256.25
272.25 + -33x + x2 = 256.25

Factor a perfect square on the left side:
(x + -16.5)(x + -16.5) = 256.25

Calculate the square root of the right side: 16.007810594

Break this problem into two subproblems by setting 
(x + -16.5) equal to 16.007810594 and -16.007810594.


Subproblem 1
x + -16.5 = 16.007810594

Simplifying
x + -16.5 = 16.007810594

Reorder the terms:
-16.5 + x = 16.007810594

Solving
-16.5 + x = 16.007810594

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 = 16.007810594 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = 16.007810594 + 16.5
x = 16.007810594 + 16.5

Combine like terms: 16.007810594 + 16.5 = 32.507810594
x = 32.507810594

Simplifying
x = 32.507810594


Subproblem 2
x + -16.5 = -16.007810594

Simplifying
x + -16.5 = -16.007810594

Reorder the terms:
-16.5 + x = -16.007810594

Solving
-16.5 + x = -16.007810594

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 = -16.007810594 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = -16.007810594 + 16.5
x = -16.007810594 + 16.5

Combine like terms: -16.007810594 + 16.5 = 0.492189406
x = 0.492189406

Simplifying
x = 0.492189406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.507810594, 0.492189406}

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