3x^2(x^2-20)=16-2x^2

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Solution for 3x^2(x^2-20)=16-2x^2 equation: 


Simplifying
3x2(x2 + -20) = 16 + -2x2

Reorder the terms:
3x2(-20 + x2) = 16 + -2x2
(-20 * 3x2 + x2 * 3x2) = 16 + -2x2
(-60x2 + 3x4) = 16 + -2x2

Solving
-60x2 + 3x4 = 16 + -2x2

Solving for variable 'x'.

Reorder the terms:
-16 + -60x2 + 2x2 + 3x4 = 16 + -2x2 + -16 + 2x2

Combine like terms: -60x2 + 2x2 = -58x2
-16 + -58x2 + 3x4 = 16 + -2x2 + -16 + 2x2

Reorder the terms:
-16 + -58x2 + 3x4 = 16 + -16 + -2x2 + 2x2

Combine like terms: 16 + -16 = 0
-16 + -58x2 + 3x4 = 0 + -2x2 + 2x2
-16 + -58x2 + 3x4 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-16 + -58x2 + 3x4 = 0

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

Divide each side by '3'.
-5.333333333 + -19.33333333x2 + x4 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -19.33333333x2 + 5.333333333 + x4 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -19.33333333x2 + x4 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -19.33333333x2 + x4 = 0 + 5.333333333
-19.33333333x2 + x4 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-19.33333333x2 + x4 = 5.333333333

The x term is -19.33333333x2.  Take half its coefficient (-9.666666665).
Square it (93.44444441) and add it to both sides.

Add '93.44444441' to each side of the equation.
-19.33333333x2 + 93.44444441 + x4 = 5.333333333 + 93.44444441

Reorder the terms:
93.44444441 + -19.33333333x2 + x4 = 5.333333333 + 93.44444441

Combine like terms: 5.333333333 + 93.44444441 = 98.777777743
93.44444441 + -19.33333333x2 + x4 = 98.777777743

Factor a perfect square on the left side:
(x2 + -9.666666665)(x2 + -9.666666665) = 98.777777743

Calculate the square root of the right side: 9.938701009

Break this problem into two subproblems by setting 
(x2 + -9.666666665) equal to 9.938701009 and -9.938701009.


Subproblem 1
x2 + -9.666666665 = 9.938701009

Simplifying
x2 + -9.666666665 = 9.938701009

Reorder the terms:
-9.666666665 + x2 = 9.938701009

Solving
-9.666666665 + x2 = 9.938701009

Solving for variable 'x'.

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

Add '9.666666665' to each side of the equation.
-9.666666665 + 9.666666665 + x2 = 9.938701009 + 9.666666665

Combine like terms: -9.666666665 + 9.666666665 = 0.000000000
0.000000000 + x2 = 9.938701009 + 9.666666665
x2 = 9.938701009 + 9.666666665

Combine like terms: 9.938701009 + 9.666666665 = 19.605367674
x2 = 19.605367674

Simplifying
x2 = 19.605367674

Take the square root of each side:
x = {-4.4277949, 4.4277949}


Subproblem 2
x2 + -9.666666665 = -9.938701009

Simplifying
x2 + -9.666666665 = -9.938701009

Reorder the terms:
-9.666666665 + x2 = -9.938701009

Solving
-9.666666665 + x2 = -9.938701009

Solving for variable 'x'.

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

Add '9.666666665' to each side of the equation.
-9.666666665 + 9.666666665 + x2 = -9.938701009 + 9.666666665

Combine like terms: -9.666666665 + 9.666666665 = 0.000000000
0.000000000 + x2 = -9.938701009 + 9.666666665
x2 = -9.938701009 + 9.666666665

Combine like terms: -9.938701009 + 9.666666665 = -0.272034344
x2 = -0.272034344

Simplifying
x2 = -0.272034344

Reorder the terms:
0.272034344 + x2 = -0.272034344 + 0.272034344

Combine like terms: -0.272034344 + 0.272034344 = 0.000000000
0.272034344 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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