4x^4+2x^2-1=0

Simple and best practice solution for 4x^4+2x^2-1=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4x^4+2x^2-1=0 equation: 


Simplifying
4x4 + 2x2 + -1 = 0

Reorder the terms:
-1 + 2x2 + 4x4 = 0

Solving
-1 + 2x2 + 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'.
-0.25 + 0.5x2 + x4 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.5x2 + 0.25 + x4 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.5x2 + x4 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.5x2 + x4 = 0 + 0.25
0.5x2 + x4 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.5x2 + x4 = 0.25

The x term is 0.5x2.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x2 + 0.0625 + x4 = 0.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x2 + x4 = 0.25 + 0.0625

Combine like terms: 0.25 + 0.0625 = 0.3125
0.0625 + 0.5x2 + x4 = 0.3125

Factor a perfect square on the left side:
(x2 + 0.25)(x2 + 0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x2 + 0.25) equal to 0.559016994 and -0.559016994.


Subproblem 1
x2 + 0.25 = 0.559016994

Simplifying
x2 + 0.25 = 0.559016994

Reorder the terms:
0.25 + x2 = 0.559016994

Solving
0.25 + x2 = 0.559016994

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x2 = 0.559016994 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x2 = 0.559016994 + -0.25
x2 = 0.559016994 + -0.25

Combine like terms: 0.559016994 + -0.25 = 0.309016994
x2 = 0.309016994

Simplifying
x2 = 0.309016994

Take the square root of each side:
x = {-0.55589297, 0.55589297}


Subproblem 2
x2 + 0.25 = -0.559016994

Simplifying
x2 + 0.25 = -0.559016994

Reorder the terms:
0.25 + x2 = -0.559016994

Solving
0.25 + x2 = -0.559016994

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x2 = -0.559016994 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x2 = -0.559016994 + -0.25
x2 = -0.559016994 + -0.25

Combine like terms: -0.559016994 + -0.25 = -0.809016994
x2 = -0.809016994

Simplifying
x2 = -0.809016994

Reorder the terms:
0.809016994 + x2 = -0.809016994 + 0.809016994

Combine like terms: -0.809016994 + 0.809016994 = 0.000000000
0.809016994 + 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.

See similar equations:

| a*6=5 | | X(x)+6x+4=0 | | x-0.95=-3.6 | | x^2+2x=36 | | 25+4y-20=19y-10 | | 6x+32=11x-3 | | -4x+8y=56 | | X-2+x-2+x-2=294 | | 3x-8=8-33 | | -6y+5=-12 | | x-2=4-2 | | 4(n+2)(n+5)=0 | | 3q^2=-5 | | 0.4+2=24 | | 4x=log(3)8x-2 | | 10y=-20 | | -6-x=0 | | 3x=(78,6*5)2 | | x=(78,6*5)2 | | y-4=5 | | k^2-3k=10 | | 3z-2z-6= | | 15-4(x-3)=x-3 | | 13+9x=-21x-17 | | 3z-2z+6= | | 7x-4=3x+2(x+3) | | -5-5y=-20 | | 0-5y=-20 | | z+2=10 | | 5m+10n= | | 9=6-2x | | 12+4y=8 |

Equations solver categories