x^2-48x-144=0

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Solution for x^2-48x-144=0 equation: 


Simplifying
x2 + -48x + -144 = 0

Reorder the terms:
-144 + -48x + x2 = 0

Solving
-144 + -48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + -48x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + -48x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + -48x + x2 = 0 + 144
-48x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
-48x + x2 = 144

The x term is -48x.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48x + 576 + x2 = 144 + 576

Reorder the terms:
576 + -48x + x2 = 144 + 576

Combine like terms: 144 + 576 = 720
576 + -48x + x2 = 720

Factor a perfect square on the left side:
(x + -24)(x + -24) = 720

Calculate the square root of the right side: 26.83281573

Break this problem into two subproblems by setting 
(x + -24) equal to 26.83281573 and -26.83281573.


Subproblem 1
x + -24 = 26.83281573

Simplifying
x + -24 = 26.83281573

Reorder the terms:
-24 + x = 26.83281573

Solving
-24 + x = 26.83281573

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = 26.83281573 + 24

Combine like terms: -24 + 24 = 0
0 + x = 26.83281573 + 24
x = 26.83281573 + 24

Combine like terms: 26.83281573 + 24 = 50.83281573
x = 50.83281573

Simplifying
x = 50.83281573


Subproblem 2
x + -24 = -26.83281573

Simplifying
x + -24 = -26.83281573

Reorder the terms:
-24 + x = -26.83281573

Solving
-24 + x = -26.83281573

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = -26.83281573 + 24

Combine like terms: -24 + 24 = 0
0 + x = -26.83281573 + 24
x = -26.83281573 + 24

Combine like terms: -26.83281573 + 24 = -2.83281573
x = -2.83281573

Simplifying
x = -2.83281573


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.83281573, -2.83281573}

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