x^2-6x-32764=0

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Solution for x^2-6x-32764=0 equation:


Simplifying
x2 + -6x + -32764 = 0

Reorder the terms:
-32764 + -6x + x2 = 0

Solving
-32764 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '32764' to each side of the equation.
-32764 + -6x + 32764 + x2 = 0 + 32764

Reorder the terms:
-32764 + 32764 + -6x + x2 = 0 + 32764

Combine like terms: -32764 + 32764 = 0
0 + -6x + x2 = 0 + 32764
-6x + x2 = 0 + 32764

Combine like terms: 0 + 32764 = 32764
-6x + x2 = 32764

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 32764 + 9

Reorder the terms:
9 + -6x + x2 = 32764 + 9

Combine like terms: 32764 + 9 = 32773
9 + -6x + x2 = 32773

Factor a perfect square on the left side:
(x + -3)(x + -3) = 32773

Calculate the square root of the right side: 181.033146136

Break this problem into two subproblems by setting 
(x + -3) equal to 181.033146136 and -181.033146136.


Subproblem 1
x + -3 = 181.033146136

Simplifying
x + -3 = 181.033146136

Reorder the terms:
-3 + x = 181.033146136

Solving
-3 + x = 181.033146136

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 181.033146136 + 3

Combine like terms: -3 + 3 = 0
0 + x = 181.033146136 + 3
x = 181.033146136 + 3

Combine like terms: 181.033146136 + 3 = 184.033146136
x = 184.033146136

Simplifying
x = 184.033146136


Subproblem 2
x + -3 = -181.033146136

Simplifying
x + -3 = -181.033146136

Reorder the terms:
-3 + x = -181.033146136

Solving
-3 + x = -181.033146136

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -181.033146136 + 3

Combine like terms: -3 + 3 = 0
0 + x = -181.033146136 + 3
x = -181.033146136 + 3

Combine like terms: -181.033146136 + 3 = -178.033146136
x = -178.033146136

Simplifying
x = -178.033146136


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {184.033146136, -178.033146136}

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