1600=x^2+48*x+576

Solution for 1600=x^2+48*x+576 equation:

Simplifying
1600 = x2 + 48x + 576

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

Solving
1600 = 576 + 48x + x2

Solving for variable 'x'.

Combine like terms: 1600 + -576 = 1024
1024 + -48x + -1x2 = 576 + 48x + x2 + -576 + -48x + -1x2

Reorder the terms:
1024 + -48x + -1x2 = 576 + -576 + 48x + -48x + x2 + -1x2

Combine like terms: 576 + -576 = 0
1024 + -48x + -1x2 = 0 + 48x + -48x + x2 + -1x2
1024 + -48x + -1x2 = 48x + -48x + x2 + -1x2

Combine like terms: 48x + -48x = 0
1024 + -48x + -1x2 = 0 + x2 + -1x2
1024 + -48x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1024 + -48x + -1x2 = 0

Factor a trinomial.
(16 + -1x)(64 + x) = 0

Subproblem 1
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Subproblem 2
Set the factor '(64 + x)' equal to zero and attempt to solve:

Simplifying
64 + x = 0

Solving
64 + x = 0

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

Add '-64' to each side of the equation.
64 + -64 + x = 0 + -64

Combine like terms: 64 + -64 = 0
0 + x = 0 + -64
x = 0 + -64

Combine like terms: 0 + -64 = -64
x = -64

Simplifying
x = -64
Solution
x = {16, -64}