x^2+x^2-4x-4x+16=4x^2-16x-16x+64

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Solution for x^2+x^2-4x-4x+16=4x^2-16x-16x+64 equation: 


Simplifying
x2 + x2 + -4x + -4x + 16 = 4x2 + -16x + -16x + 64

Reorder the terms:
16 + -4x + -4x + x2 + x2 = 4x2 + -16x + -16x + 64

Combine like terms: -4x + -4x = -8x
16 + -8x + x2 + x2 = 4x2 + -16x + -16x + 64

Combine like terms: x2 + x2 = 2x2
16 + -8x + 2x2 = 4x2 + -16x + -16x + 64

Reorder the terms:
16 + -8x + 2x2 = 64 + -16x + -16x + 4x2

Combine like terms: -16x + -16x = -32x
16 + -8x + 2x2 = 64 + -32x + 4x2

Solving
16 + -8x + 2x2 = 64 + -32x + 4x2

Solving for variable 'x'.

Reorder the terms:
16 + -64 + -8x + 32x + 2x2 + -4x2 = 64 + -32x + 4x2 + -64 + 32x + -4x2

Combine like terms: 16 + -64 = -48
-48 + -8x + 32x + 2x2 + -4x2 = 64 + -32x + 4x2 + -64 + 32x + -4x2

Combine like terms: -8x + 32x = 24x
-48 + 24x + 2x2 + -4x2 = 64 + -32x + 4x2 + -64 + 32x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-48 + 24x + -2x2 = 64 + -32x + 4x2 + -64 + 32x + -4x2

Reorder the terms:
-48 + 24x + -2x2 = 64 + -64 + -32x + 32x + 4x2 + -4x2

Combine like terms: 64 + -64 = 0
-48 + 24x + -2x2 = 0 + -32x + 32x + 4x2 + -4x2
-48 + 24x + -2x2 = -32x + 32x + 4x2 + -4x2

Combine like terms: -32x + 32x = 0
-48 + 24x + -2x2 = 0 + 4x2 + -4x2
-48 + 24x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-48 + 24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 12x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + 12x + -1x2)' equal to zero and attempt to solve:

Simplifying
-24 + 12x + -1x2 = 0

Solving
-24 + 12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
24 + -12x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -12x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -12x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -12x + x2 = 0 + -24
-12x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-12x + x2 = -24

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 = -24 + 36

Reorder the terms:
36 + -12x + x2 = -24 + 36

Combine like terms: -24 + 36 = 12
36 + -12x + x2 = 12

Factor a perfect square on the left side:
(x + -6)(x + -6) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -6) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + -6 = 3.464101615

Simplifying
x + -6 = 3.464101615

Reorder the terms:
-6 + x = 3.464101615

Solving
-6 + x = 3.464101615

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 = 3.464101615 + 6

Combine like terms: -6 + 6 = 0
0 + x = 3.464101615 + 6
x = 3.464101615 + 6

Combine like terms: 3.464101615 + 6 = 9.464101615
x = 9.464101615

Simplifying
x = 9.464101615


Subproblem 2
x + -6 = -3.464101615

Simplifying
x + -6 = -3.464101615

Reorder the terms:
-6 + x = -3.464101615

Solving
-6 + x = -3.464101615

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 = -3.464101615 + 6

Combine like terms: -6 + 6 = 0
0 + x = -3.464101615 + 6
x = -3.464101615 + 6

Combine like terms: -3.464101615 + 6 = 2.535898385
x = 2.535898385

Simplifying
x = 2.535898385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.464101615, 2.535898385}
Solution
x = {9.464101615, 2.535898385}

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