4x^4+65x^2-16=0

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Solution for 4x^4+65x^2-16=0 equation: 


Simplifying
4x4 + 65x2 + -16 = 0

Reorder the terms:
-16 + 65x2 + 4x4 = 0

Solving
-16 + 65x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-4 + 16.25x2 + x4 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 16.25x2 + 4 + x4 = 0 + 4

Reorder the terms:
-4 + 4 + 16.25x2 + x4 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 16.25x2 + x4 = 0 + 4
16.25x2 + x4 = 0 + 4

Combine like terms: 0 + 4 = 4
16.25x2 + x4 = 4

The x term is 16.25x2.  Take half its coefficient (8.125).
Square it (66.015625) and add it to both sides.

Add '66.015625' to each side of the equation.
16.25x2 + 66.015625 + x4 = 4 + 66.015625

Reorder the terms:
66.015625 + 16.25x2 + x4 = 4 + 66.015625

Combine like terms: 4 + 66.015625 = 70.015625
66.015625 + 16.25x2 + x4 = 70.015625

Factor a perfect square on the left side:
(x2 + 8.125)(x2 + 8.125) = 70.015625

Calculate the square root of the right side: 8.367533986

Break this problem into two subproblems by setting 
(x2 + 8.125) equal to 8.367533986 and -8.367533986.


Subproblem 1
x2 + 8.125 = 8.367533986

Simplifying
x2 + 8.125 = 8.367533986

Reorder the terms:
8.125 + x2 = 8.367533986

Solving
8.125 + x2 = 8.367533986

Solving for variable 'x'.

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

Add '-8.125' to each side of the equation.
8.125 + -8.125 + x2 = 8.367533986 + -8.125

Combine like terms: 8.125 + -8.125 = 0.000
0.000 + x2 = 8.367533986 + -8.125
x2 = 8.367533986 + -8.125

Combine like terms: 8.367533986 + -8.125 = 0.242533986
x2 = 0.242533986

Simplifying
x2 = 0.242533986

Take the square root of each side:
x = {-0.492477396, 0.492477396}


Subproblem 2
x2 + 8.125 = -8.367533986

Simplifying
x2 + 8.125 = -8.367533986

Reorder the terms:
8.125 + x2 = -8.367533986

Solving
8.125 + x2 = -8.367533986

Solving for variable 'x'.

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

Add '-8.125' to each side of the equation.
8.125 + -8.125 + x2 = -8.367533986 + -8.125

Combine like terms: 8.125 + -8.125 = 0.000
0.000 + x2 = -8.367533986 + -8.125
x2 = -8.367533986 + -8.125

Combine like terms: -8.367533986 + -8.125 = -16.492533986
x2 = -16.492533986

Simplifying
x2 = -16.492533986

Reorder the terms:
16.492533986 + x2 = -16.492533986 + 16.492533986

Combine like terms: -16.492533986 + 16.492533986 = 0.000000000
16.492533986 + 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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