3x^4-19x^2-16=0

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Solution for 3x^4-19x^2-16=0 equation: 


Simplifying
3x4 + -19x2 + -16 = 0

Reorder the terms:
-16 + -19x2 + 3x4 = 0

Solving
-16 + -19x2 + 3x4 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-5.333333333 + -6.333333333x2 + x4 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -6.333333333x2 + 5.333333333 + x4 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -6.333333333x2 + x4 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -6.333333333x2 + x4 = 0 + 5.333333333
-6.333333333x2 + x4 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-6.333333333x2 + x4 = 5.333333333

The x term is -6.333333333x2.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x2 + 10.02777778 + x4 = 5.333333333 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x2 + x4 = 5.333333333 + 10.02777778

Combine like terms: 5.333333333 + 10.02777778 = 15.361111113
10.02777778 + -6.333333333x2 + x4 = 15.361111113

Factor a perfect square on the left side:
(x2 + -3.166666667)(x2 + -3.166666667) = 15.361111113

Calculate the square root of the right side: 3.919325339

Break this problem into two subproblems by setting 
(x2 + -3.166666667) equal to 3.919325339 and -3.919325339.


Subproblem 1
x2 + -3.166666667 = 3.919325339

Simplifying
x2 + -3.166666667 = 3.919325339

Reorder the terms:
-3.166666667 + x2 = 3.919325339

Solving
-3.166666667 + x2 = 3.919325339

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x2 = 3.919325339 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x2 = 3.919325339 + 3.166666667
x2 = 3.919325339 + 3.166666667

Combine like terms: 3.919325339 + 3.166666667 = 7.085992006
x2 = 7.085992006

Simplifying
x2 = 7.085992006

Take the square root of each side:
x = {-2.661952668, 2.661952668}


Subproblem 2
x2 + -3.166666667 = -3.919325339

Simplifying
x2 + -3.166666667 = -3.919325339

Reorder the terms:
-3.166666667 + x2 = -3.919325339

Solving
-3.166666667 + x2 = -3.919325339

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x2 = -3.919325339 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x2 = -3.919325339 + 3.166666667
x2 = -3.919325339 + 3.166666667

Combine like terms: -3.919325339 + 3.166666667 = -0.752658672
x2 = -0.752658672

Simplifying
x2 = -0.752658672

Reorder the terms:
0.752658672 + x2 = -0.752658672 + 0.752658672

Combine like terms: -0.752658672 + 0.752658672 = 0.000000000
0.752658672 + 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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