x^2+16x-3584=0

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Solution for x^2+16x-3584=0 equation: 


Simplifying
x2 + 16x + -3584 = 0

Reorder the terms:
-3584 + 16x + x2 = 0

Solving
-3584 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3584' to each side of the equation.
-3584 + 16x + 3584 + x2 = 0 + 3584

Reorder the terms:
-3584 + 3584 + 16x + x2 = 0 + 3584

Combine like terms: -3584 + 3584 = 0
0 + 16x + x2 = 0 + 3584
16x + x2 = 0 + 3584

Combine like terms: 0 + 3584 = 3584
16x + x2 = 3584

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 3584 + 64

Reorder the terms:
64 + 16x + x2 = 3584 + 64

Combine like terms: 3584 + 64 = 3648
64 + 16x + x2 = 3648

Factor a perfect square on the left side:
(x + 8)(x + 8) = 3648

Calculate the square root of the right side: 60.398675482

Break this problem into two subproblems by setting 
(x + 8) equal to 60.398675482 and -60.398675482.


Subproblem 1
x + 8 = 60.398675482

Simplifying
x + 8 = 60.398675482

Reorder the terms:
8 + x = 60.398675482

Solving
8 + x = 60.398675482

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 60.398675482 + -8

Combine like terms: 8 + -8 = 0
0 + x = 60.398675482 + -8
x = 60.398675482 + -8

Combine like terms: 60.398675482 + -8 = 52.398675482
x = 52.398675482

Simplifying
x = 52.398675482


Subproblem 2
x + 8 = -60.398675482

Simplifying
x + 8 = -60.398675482

Reorder the terms:
8 + x = -60.398675482

Solving
8 + x = -60.398675482

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -60.398675482 + -8

Combine like terms: 8 + -8 = 0
0 + x = -60.398675482 + -8
x = -60.398675482 + -8

Combine like terms: -60.398675482 + -8 = -68.398675482
x = -68.398675482

Simplifying
x = -68.398675482


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {52.398675482, -68.398675482}

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