x^2+16x-48=0

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Solution for x^2+16x-48=0 equation: 


Simplifying
x2 + 16x + -48 = 0

Reorder the terms:
-48 + 16x + x2 = 0

Solving
-48 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 16x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 16x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 16x + x2 = 0 + 48
16x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
16x + x2 = 48

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 = 48 + 64

Reorder the terms:
64 + 16x + x2 = 48 + 64

Combine like terms: 48 + 64 = 112
64 + 16x + x2 = 112

Factor a perfect square on the left side:
(x + 8)(x + 8) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + 8) equal to 10.583005244 and -10.583005244.


Subproblem 1
x + 8 = 10.583005244

Simplifying
x + 8 = 10.583005244

Reorder the terms:
8 + x = 10.583005244

Solving
8 + x = 10.583005244

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 = 10.583005244 + -8

Combine like terms: 8 + -8 = 0
0 + x = 10.583005244 + -8
x = 10.583005244 + -8

Combine like terms: 10.583005244 + -8 = 2.583005244
x = 2.583005244

Simplifying
x = 2.583005244


Subproblem 2
x + 8 = -10.583005244

Simplifying
x + 8 = -10.583005244

Reorder the terms:
8 + x = -10.583005244

Solving
8 + x = -10.583005244

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 = -10.583005244 + -8

Combine like terms: 8 + -8 = 0
0 + x = -10.583005244 + -8
x = -10.583005244 + -8

Combine like terms: -10.583005244 + -8 = -18.583005244
x = -18.583005244

Simplifying
x = -18.583005244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.583005244, -18.583005244}

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