x^2-4x-48000=0

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Solution for x^2-4x-48000=0 equation: 


Simplifying
x2 + -4x + -48000 = 0

Reorder the terms:
-48000 + -4x + x2 = 0

Solving
-48000 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '48000' to each side of the equation.
-48000 + -4x + 48000 + x2 = 0 + 48000

Reorder the terms:
-48000 + 48000 + -4x + x2 = 0 + 48000

Combine like terms: -48000 + 48000 = 0
0 + -4x + x2 = 0 + 48000
-4x + x2 = 0 + 48000

Combine like terms: 0 + 48000 = 48000
-4x + x2 = 48000

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 48000 + 4

Reorder the terms:
4 + -4x + x2 = 48000 + 4

Combine like terms: 48000 + 4 = 48004
4 + -4x + x2 = 48004

Factor a perfect square on the left side:
(x + -2)(x + -2) = 48004

Calculate the square root of the right side: 219.098151521

Break this problem into two subproblems by setting 
(x + -2) equal to 219.098151521 and -219.098151521.


Subproblem 1
x + -2 = 219.098151521

Simplifying
x + -2 = 219.098151521

Reorder the terms:
-2 + x = 219.098151521

Solving
-2 + x = 219.098151521

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 219.098151521 + 2

Combine like terms: -2 + 2 = 0
0 + x = 219.098151521 + 2
x = 219.098151521 + 2

Combine like terms: 219.098151521 + 2 = 221.098151521
x = 221.098151521

Simplifying
x = 221.098151521


Subproblem 2
x + -2 = -219.098151521

Simplifying
x + -2 = -219.098151521

Reorder the terms:
-2 + x = -219.098151521

Solving
-2 + x = -219.098151521

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -219.098151521 + 2

Combine like terms: -2 + 2 = 0
0 + x = -219.098151521 + 2
x = -219.098151521 + 2

Combine like terms: -219.098151521 + 2 = -217.098151521
x = -217.098151521

Simplifying
x = -217.098151521


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {221.098151521, -217.098151521}

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