Z^4+2*Z^2-2=0

Simple and best practice solution for Z^4+2*Z^2-2=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 Z^4+2*Z^2-2=0 equation:


Simplifying
Z4 + 2Z2 + -2 = 0

Reorder the terms:
-2 + 2Z2 + Z4 = 0

Solving
-2 + 2Z2 + Z4 = 0

Solving for variable 'Z'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2Z2 + 2 + Z4 = 0 + 2

Reorder the terms:
-2 + 2 + 2Z2 + Z4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2Z2 + Z4 = 0 + 2
2Z2 + Z4 = 0 + 2

Combine like terms: 0 + 2 = 2
2Z2 + Z4 = 2

The Z term is 2Z2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2Z2 + 1 + Z4 = 2 + 1

Reorder the terms:
1 + 2Z2 + Z4 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + 2Z2 + Z4 = 3

Factor a perfect square on the left side:
(Z2 + 1)(Z2 + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(Z2 + 1) equal to 1.732050808 and -1.732050808.

Subproblem 1

Z2 + 1 = 1.732050808 Simplifying Z2 + 1 = 1.732050808 Reorder the terms: 1 + Z2 = 1.732050808 Solving 1 + Z2 = 1.732050808 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + Z2 = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + Z2 = 1.732050808 + -1 Z2 = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 Z2 = 0.732050808 Simplifying Z2 = 0.732050808 Take the square root of each side: Z = {-0.855599677, 0.855599677}

Subproblem 2

Z2 + 1 = -1.732050808 Simplifying Z2 + 1 = -1.732050808 Reorder the terms: 1 + Z2 = -1.732050808 Solving 1 + Z2 = -1.732050808 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + Z2 = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + Z2 = -1.732050808 + -1 Z2 = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 Z2 = -2.732050808 Simplifying Z2 = -2.732050808 Reorder the terms: 2.732050808 + Z2 = -2.732050808 + 2.732050808 Combine like terms: -2.732050808 + 2.732050808 = 0.000000000 2.732050808 + Z2 = 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+-7+-9a+-2a+-10= | | -3=5.7 | | 11-8y+16=x+12y-2x | | 5d=36.6 | | 5k-10-8k=-35 | | 30=-2+4x | | X=Y^3-14y^2+45y | | 13/3x11/5 | | 2(3x)-5=22 | | 4x^2+16*x=20 | | 324.09=9(0.08m+26.70+0.10(26.70)) | | 4(w+2)-7w=14 | | 12x=7y+3 | | 5*w^2+10*w=40 | | 7xy^4+14x^3y^2= | | X^2-8x+y^2+2y=28 | | 2(7+10c)= | | 3*m*2p= | | 7x=-24-8y | | 4x^2+5x=-5 | | (2x)/3=48/(2x) | | s^2+3s=-9 | | 5x+1+3x+9=90 | | Y=-7+32 | | 3x+.66y=6 | | 10+-9+-5+-10w= | | (6n-15)-(3n-6)= | | X/8=62 | | 2y=X-11 | | -16t^2+128t=220 | | -32=-85 | | 36+x-24=360 |

Equations solver categories