x^2+x^2+12x+36+8x-48+16=2

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Solution for x^2+x^2+12x+36+8x-48+16=2 equation: 


Simplifying
x2 + x2 + 12x + 36 + 8x + -48 + 16 = 2

Reorder the terms:
36 + -48 + 16 + 12x + 8x + x2 + x2 = 2

Combine like terms: 36 + -48 = -12
-12 + 16 + 12x + 8x + x2 + x2 = 2

Combine like terms: -12 + 16 = 4
4 + 12x + 8x + x2 + x2 = 2

Combine like terms: 12x + 8x = 20x
4 + 20x + x2 + x2 = 2

Combine like terms: x2 + x2 = 2x2
4 + 20x + 2x2 = 2

Solving
4 + 20x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
4 + -2 + 20x + 2x2 = 2 + -2

Combine like terms: 4 + -2 = 2
2 + 20x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
2 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
1 + 10x + x2 = 0

Solving
1 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 10x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 10x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10x + x2 = 0 + -1
10x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
10x + x2 = -1

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -1 + 25

Reorder the terms:
25 + 10x + x2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + 10x + x2 = 24

Factor a perfect square on the left side:
(x + 5)(x + 5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 5) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + 5 = 4.898979486

Simplifying
x + 5 = 4.898979486

Reorder the terms:
5 + x = 4.898979486

Solving
5 + x = 4.898979486

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 4.898979486 + -5

Combine like terms: 5 + -5 = 0
0 + x = 4.898979486 + -5
x = 4.898979486 + -5

Combine like terms: 4.898979486 + -5 = -0.101020514
x = -0.101020514

Simplifying
x = -0.101020514


Subproblem 2
x + 5 = -4.898979486

Simplifying
x + 5 = -4.898979486

Reorder the terms:
5 + x = -4.898979486

Solving
5 + x = -4.898979486

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -4.898979486 + -5

Combine like terms: 5 + -5 = 0
0 + x = -4.898979486 + -5
x = -4.898979486 + -5

Combine like terms: -4.898979486 + -5 = -9.898979486
x = -9.898979486

Simplifying
x = -9.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.101020514, -9.898979486}
Solution
x = {-0.101020514, -9.898979486}

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