-12x-2=x^2+16

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Solution for -12x-2=x^2+16 equation: 


Simplifying
-12x + -2 = x2 + 16

Reorder the terms:
-2 + -12x = x2 + 16

Reorder the terms:
-2 + -12x = 16 + x2

Solving
-2 + -12x = 16 + x2

Solving for variable 'x'.

Reorder the terms:
-2 + -16 + -12x + -1x2 = 16 + x2 + -16 + -1x2

Combine like terms: -2 + -16 = -18
-18 + -12x + -1x2 = 16 + x2 + -16 + -1x2

Reorder the terms:
-18 + -12x + -1x2 = 16 + -16 + x2 + -1x2

Combine like terms: 16 + -16 = 0
-18 + -12x + -1x2 = 0 + x2 + -1x2
-18 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 12x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(18 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
18 + 12x + x2 = 0

Solving
18 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 12x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 12x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 12x + x2 = 0 + -18
12x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
12x + x2 = -18

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -18 + 36

Reorder the terms:
36 + 12x + x2 = -18 + 36

Combine like terms: -18 + 36 = 18
36 + 12x + x2 = 18

Factor a perfect square on the left side:
(x + 6)(x + 6) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 6) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 6 = 4.242640687

Simplifying
x + 6 = 4.242640687

Reorder the terms:
6 + x = 4.242640687

Solving
6 + x = 4.242640687

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 4.242640687 + -6

Combine like terms: 6 + -6 = 0
0 + x = 4.242640687 + -6
x = 4.242640687 + -6

Combine like terms: 4.242640687 + -6 = -1.757359313
x = -1.757359313

Simplifying
x = -1.757359313


Subproblem 2
x + 6 = -4.242640687

Simplifying
x + 6 = -4.242640687

Reorder the terms:
6 + x = -4.242640687

Solving
6 + x = -4.242640687

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -4.242640687 + -6

Combine like terms: 6 + -6 = 0
0 + x = -4.242640687 + -6
x = -4.242640687 + -6

Combine like terms: -4.242640687 + -6 = -10.242640687
x = -10.242640687

Simplifying
x = -10.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.757359313, -10.242640687}
Solution
x = {-1.757359313, -10.242640687}

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