47x^2-6x^4-8=0

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Solution for 47x^2-6x^4-8=0 equation: 


Simplifying
47x2 + -6x4 + -8 = 0

Reorder the terms:
-8 + 47x2 + -6x4 = 0

Solving
-8 + 47x2 + -6x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
1.333333333 + -7.833333333x2 + x4 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -7.833333333x2 + -1.333333333 + x4 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -7.833333333x2 + x4 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -7.833333333x2 + x4 = 0 + -1.333333333
-7.833333333x2 + x4 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-7.833333333x2 + x4 = -1.333333333

The x term is -7.833333333x2.  Take half its coefficient (-3.916666667).
Square it (15.34027778) and add it to both sides.

Add '15.34027778' to each side of the equation.
-7.833333333x2 + 15.34027778 + x4 = -1.333333333 + 15.34027778

Reorder the terms:
15.34027778 + -7.833333333x2 + x4 = -1.333333333 + 15.34027778

Combine like terms: -1.333333333 + 15.34027778 = 14.006944447
15.34027778 + -7.833333333x2 + x4 = 14.006944447

Factor a perfect square on the left side:
(x2 + -3.916666667)(x2 + -3.916666667) = 14.006944447

Calculate the square root of the right side: 3.742585262

Break this problem into two subproblems by setting 
(x2 + -3.916666667) equal to 3.742585262 and -3.742585262.


Subproblem 1
x2 + -3.916666667 = 3.742585262

Simplifying
x2 + -3.916666667 = 3.742585262

Reorder the terms:
-3.916666667 + x2 = 3.742585262

Solving
-3.916666667 + x2 = 3.742585262

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x2 = 3.742585262 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x2 = 3.742585262 + 3.916666667
x2 = 3.742585262 + 3.916666667

Combine like terms: 3.742585262 + 3.916666667 = 7.659251929
x2 = 7.659251929

Simplifying
x2 = 7.659251929

Take the square root of each side:
x = {-2.767535353, 2.767535353}


Subproblem 2
x2 + -3.916666667 = -3.742585262

Simplifying
x2 + -3.916666667 = -3.742585262

Reorder the terms:
-3.916666667 + x2 = -3.742585262

Solving
-3.916666667 + x2 = -3.742585262

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x2 = -3.742585262 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x2 = -3.742585262 + 3.916666667
x2 = -3.742585262 + 3.916666667

Combine like terms: -3.742585262 + 3.916666667 = 0.174081405
x2 = 0.174081405

Simplifying
x2 = 0.174081405

Take the square root of each side:
x = {-0.417230638, 0.417230638}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.767535353, 2.767535353, -0.417230638, 0.417230638}

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