x^2-504x-4=0

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Solution for x^2-504x-4=0 equation: 


Simplifying
x2 + -504x + -4 = 0

Reorder the terms:
-4 + -504x + x2 = 0

Solving
-4 + -504x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -504x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -504x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -504x + x2 = 0 + 4
-504x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-504x + x2 = 4

The x term is -504x.  Take half its coefficient (-252).
Square it (63504) and add it to both sides.

Add '63504' to each side of the equation.
-504x + 63504 + x2 = 4 + 63504

Reorder the terms:
63504 + -504x + x2 = 4 + 63504

Combine like terms: 4 + 63504 = 63508
63504 + -504x + x2 = 63508

Factor a perfect square on the left side:
(x + -252)(x + -252) = 63508

Calculate the square root of the right side: 252.007936383

Break this problem into two subproblems by setting 
(x + -252) equal to 252.007936383 and -252.007936383.


Subproblem 1
x + -252 = 252.007936383

Simplifying
x + -252 = 252.007936383

Reorder the terms:
-252 + x = 252.007936383

Solving
-252 + x = 252.007936383

Solving for variable 'x'.

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

Add '252' to each side of the equation.
-252 + 252 + x = 252.007936383 + 252

Combine like terms: -252 + 252 = 0
0 + x = 252.007936383 + 252
x = 252.007936383 + 252

Combine like terms: 252.007936383 + 252 = 504.007936383
x = 504.007936383

Simplifying
x = 504.007936383


Subproblem 2
x + -252 = -252.007936383

Simplifying
x + -252 = -252.007936383

Reorder the terms:
-252 + x = -252.007936383

Solving
-252 + x = -252.007936383

Solving for variable 'x'.

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

Add '252' to each side of the equation.
-252 + 252 + x = -252.007936383 + 252

Combine like terms: -252 + 252 = 0
0 + x = -252.007936383 + 252
x = -252.007936383 + 252

Combine like terms: -252.007936383 + 252 = -0.007936383
x = -0.007936383

Simplifying
x = -0.007936383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {504.007936383, -0.007936383}

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