z^6+4z^3+2=0

Simple and best practice solution for z^6+4z^3+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^6+4z^3+2=0 equation: 


Simplifying
z6 + 4z3 + 2 = 0

Reorder the terms:
2 + 4z3 + z6 = 0

Solving
2 + 4z3 + z6 = 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 + 4z3 + -2 + z6 = 0 + -2

Reorder the terms:
2 + -2 + 4z3 + z6 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4z3 + z6 = 0 + -2
4z3 + z6 = 0 + -2

Combine like terms: 0 + -2 = -2
4z3 + z6 = -2

The z term is 4z3.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4z3 + 4 + z6 = -2 + 4

Reorder the terms:
4 + 4z3 + z6 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + 4z3 + z6 = 2

Factor a perfect square on the left side:
(z3 + 2)(z3 + 2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(z3 + 2) equal to 1.414213562 and -1.414213562.


Subproblem 1
z3 + 2 = 1.414213562

Simplifying
z3 + 2 = 1.414213562

Reorder the terms:
2 + z3 = 1.414213562

Solving
2 + z3 = 1.414213562

Solving for variable 'z'.

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

Add '-2' to each side of the equation.
2 + -2 + z3 = 1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + z3 = 1.414213562 + -2
z3 = 1.414213562 + -2

Combine like terms: 1.414213562 + -2 = -0.585786438
z3 = -0.585786438

Simplifying
z3 = -0.585786438

Reorder the terms:
0.585786438 + z3 = -0.585786438 + 0.585786438

Combine like terms: -0.585786438 + 0.585786438 = 0.000000000
0.585786438 + z3 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
z3 + 2 = -1.414213562

Simplifying
z3 + 2 = -1.414213562

Reorder the terms:
2 + z3 = -1.414213562

Solving
2 + z3 = -1.414213562

Solving for variable 'z'.

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

Add '-2' to each side of the equation.
2 + -2 + z3 = -1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + z3 = -1.414213562 + -2
z3 = -1.414213562 + -2

Combine like terms: -1.414213562 + -2 = -3.414213562
z3 = -3.414213562

Simplifying
z3 = -3.414213562

Reorder the terms:
3.414213562 + z3 = -3.414213562 + 3.414213562

Combine like terms: -3.414213562 + 3.414213562 = 0.000000000
3.414213562 + z3 = 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:

| x-4-2(6-5x)=5(4x+8) | | X+117=70 | | 2(3-2x)=7(x-6)+8 | | 3x+5-2x+4=7x-1 | | 70=x+117 | | 9x*x+3*x-900=0 | | 122+3x-2=180 | | 26-4z=28-2z | | 3x^2+12x-6y^2+12y=3 | | 1-10p-2= | | 10+9a=26+a | | -7p+p= | | 4m-3n=5y | | z^2-(3+5i)+8i-5=0 | | -20(-10x+4)=120 | | 4m-3n=y | | 3x^3+6x^2-3x=0 | | 12=(-7)x-9 | | 2r-4+6+10r= | | -2/7(-1/2+x)=17/7 | | 2(x-7)+5x=10x-2 | | n+4+n= | | 6(1/2)+8(3/4)= | | 2n+10n= | | -(-1+x)=24 | | 6m+7=2+m | | -29=-10x+11 | | 11-12r= | | -5+2z=-13+2z | | -23(7z+2)=-529 | | 1-4r=13-2r | | 6(g-2)=h |

Equations solver categories