16x^4+79x^2=2

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Solution for 16x^4+79x^2=2 equation: 


Simplifying
16x4 + 79x2 = 2

Reorder the terms:
79x2 + 16x4 = 2

Solving
79x2 + 16x4 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 79x2 + 16x4 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 79x2 + 16x4 = 0

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

Divide each side by '16'.
-0.125 + 4.9375x2 + x4 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 4.9375x2 + 0.125 + x4 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 4.9375x2 + x4 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 4.9375x2 + x4 = 0 + 0.125
4.9375x2 + x4 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
4.9375x2 + x4 = 0.125

The x term is 4.9375x2.  Take half its coefficient (2.46875).
Square it (6.094726563) and add it to both sides.

Add '6.094726563' to each side of the equation.
4.9375x2 + 6.094726563 + x4 = 0.125 + 6.094726563

Reorder the terms:
6.094726563 + 4.9375x2 + x4 = 0.125 + 6.094726563

Combine like terms: 0.125 + 6.094726563 = 6.219726563
6.094726563 + 4.9375x2 + x4 = 6.219726563

Factor a perfect square on the left side:
(x2 + 2.46875)(x2 + 2.46875) = 6.219726563

Calculate the square root of the right side: 2.493937963

Break this problem into two subproblems by setting 
(x2 + 2.46875) equal to 2.493937963 and -2.493937963.


Subproblem 1
x2 + 2.46875 = 2.493937963

Simplifying
x2 + 2.46875 = 2.493937963

Reorder the terms:
2.46875 + x2 = 2.493937963

Solving
2.46875 + x2 = 2.493937963

Solving for variable 'x'.

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

Add '-2.46875' to each side of the equation.
2.46875 + -2.46875 + x2 = 2.493937963 + -2.46875

Combine like terms: 2.46875 + -2.46875 = 0.00000
0.00000 + x2 = 2.493937963 + -2.46875
x2 = 2.493937963 + -2.46875

Combine like terms: 2.493937963 + -2.46875 = 0.025187963
x2 = 0.025187963

Simplifying
x2 = 0.025187963

Take the square root of each side:
x = {-0.158707161, 0.158707161}


Subproblem 2
x2 + 2.46875 = -2.493937963

Simplifying
x2 + 2.46875 = -2.493937963

Reorder the terms:
2.46875 + x2 = -2.493937963

Solving
2.46875 + x2 = -2.493937963

Solving for variable 'x'.

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

Add '-2.46875' to each side of the equation.
2.46875 + -2.46875 + x2 = -2.493937963 + -2.46875

Combine like terms: 2.46875 + -2.46875 = 0.00000
0.00000 + x2 = -2.493937963 + -2.46875
x2 = -2.493937963 + -2.46875

Combine like terms: -2.493937963 + -2.46875 = -4.962687963
x2 = -4.962687963

Simplifying
x2 = -4.962687963

Reorder the terms:
4.962687963 + x2 = -4.962687963 + 4.962687963

Combine like terms: -4.962687963 + 4.962687963 = 0.000000000
4.962687963 + 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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