x^2-48x-1600=0

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Solution for x^2-48x-1600=0 equation: 


Simplifying
x2 + -48x + -1600 = 0

Reorder the terms:
-1600 + -48x + x2 = 0

Solving
-1600 + -48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1600' to each side of the equation.
-1600 + -48x + 1600 + x2 = 0 + 1600

Reorder the terms:
-1600 + 1600 + -48x + x2 = 0 + 1600

Combine like terms: -1600 + 1600 = 0
0 + -48x + x2 = 0 + 1600
-48x + x2 = 0 + 1600

Combine like terms: 0 + 1600 = 1600
-48x + x2 = 1600

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 = 1600 + 576

Reorder the terms:
576 + -48x + x2 = 1600 + 576

Combine like terms: 1600 + 576 = 2176
576 + -48x + x2 = 2176

Factor a perfect square on the left side:
(x + -24)(x + -24) = 2176

Calculate the square root of the right side: 46.647615159

Break this problem into two subproblems by setting 
(x + -24) equal to 46.647615159 and -46.647615159.


Subproblem 1
x + -24 = 46.647615159

Simplifying
x + -24 = 46.647615159

Reorder the terms:
-24 + x = 46.647615159

Solving
-24 + x = 46.647615159

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 = 46.647615159 + 24

Combine like terms: -24 + 24 = 0
0 + x = 46.647615159 + 24
x = 46.647615159 + 24

Combine like terms: 46.647615159 + 24 = 70.647615159
x = 70.647615159

Simplifying
x = 70.647615159


Subproblem 2
x + -24 = -46.647615159

Simplifying
x + -24 = -46.647615159

Reorder the terms:
-24 + x = -46.647615159

Solving
-24 + x = -46.647615159

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 = -46.647615159 + 24

Combine like terms: -24 + 24 = 0
0 + x = -46.647615159 + 24
x = -46.647615159 + 24

Combine like terms: -46.647615159 + 24 = -22.647615159
x = -22.647615159

Simplifying
x = -22.647615159


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {70.647615159, -22.647615159}

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