x^4-4x^2=4

Simple and best practice solution for x^4-4x^2=4 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 x^4-4x^2=4 equation:


Simplifying
x4 + -4x2 = 4

Reorder the terms:
-4x2 + x4 = 4

Solving
-4x2 + x4 = 4

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is -4x2.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

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

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

Combine like terms: 4 + 4 = 8
4 + -4x2 + x4 = 8

Factor a perfect square on the left side:
(x2 + -2)(x2 + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x2 + -2) equal to 2.828427125 and -2.828427125.

Subproblem 1

x2 + -2 = 2.828427125 Simplifying x2 + -2 = 2.828427125 Reorder the terms: -2 + x2 = 2.828427125 Solving -2 + x2 = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.828427125 + 2 x2 = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 x2 = 4.828427125 Simplifying x2 = 4.828427125 Take the square root of each side: x = {-2.197368227, 2.197368227}

Subproblem 2

x2 + -2 = -2.828427125 Simplifying x2 + -2 = -2.828427125 Reorder the terms: -2 + x2 = -2.828427125 Solving -2 + x2 = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.828427125 + 2 x2 = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 x2 = -0.828427125 Simplifying x2 = -0.828427125 Reorder the terms: 0.828427125 + x2 = -0.828427125 + 0.828427125 Combine like terms: -0.828427125 + 0.828427125 = 0.000000000 0.828427125 + 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:

| 2a+2ax+b=2x^2 | | 0.5a+3=a-20 | | 74.9=7(m+29) | | y^2+x^2=64 | | -3a+b+-2a+5b= | | -3a+b+2a-5b= | | 2x-14y=11 | | -3a+b+2a+5b= | | 5+6x=6x-2 | | -3x+2y+-2x-4y= | | -3x+2y+2x-4y= | | 8u-2u=18 | | 4x-2y+-3x-4y= | | 4x-2y+-3x+4y= | | (3a-2b)+(-2a-4b)= | | 255=10x+5Y | | 3a-2b+-2a-4b= | | 3a-2b+-2a+4b= | | 5l+26=18l | | (x/3)+(5/2)=4/3 | | x/3+5/2=4/3 | | 6p-12=2p+12 | | -4m^2-24m+64=0 | | 2x+18=10x | | X^2-18x-45=0 | | 4(x-3)+5x= | | 3sinx-1=4cosx | | 10(x-5)+7=10x+43 | | 4(2x-1)-5(1-3x)=6(x-3)+4x | | sinx^2+2sinx-2=cosx^2 | | 3a+2b-2a-4b= | | (b+9)=(4b-.75) |

Equations solver categories