z^4-z^2-3=0

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


Simplifying
z4 + -1z2 + -3 = 0

Reorder the terms:
-3 + -1z2 + z4 = 0

Solving
-3 + -1z2 + z4 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1z2 + 3 + z4 = 0 + 3

Reorder the terms:
-3 + 3 + -1z2 + z4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z2 + z4 = 0 + 3
-1z2 + z4 = 0 + 3

Combine like terms: 0 + 3 = 3
-1z2 + z4 = 3

The z term is -1z2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z2 + 0.25 + z4 = 3 + 0.25

Reorder the terms:
0.25 + -1z2 + z4 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1z2 + z4 = 3.25

Factor a perfect square on the left side:
(z2 + -0.5)(z2 + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(z2 + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

z2 + -0.5 = 1.802775638 Simplifying z2 + -0.5 = 1.802775638 Reorder the terms: -0.5 + z2 = 1.802775638 Solving -0.5 + z2 = 1.802775638 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z2 = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z2 = 1.802775638 + 0.5 z2 = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 z2 = 2.302775638 Simplifying z2 = 2.302775638 Take the square root of each side: z = {-1.517489914, 1.517489914}

Subproblem 2

z2 + -0.5 = -1.802775638 Simplifying z2 + -0.5 = -1.802775638 Reorder the terms: -0.5 + z2 = -1.802775638 Solving -0.5 + z2 = -1.802775638 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z2 = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z2 = -1.802775638 + 0.5 z2 = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 z2 = -1.302775638 Simplifying z2 = -1.302775638 Reorder the terms: 1.302775638 + z2 = -1.302775638 + 1.302775638 Combine like terms: -1.302775638 + 1.302775638 = 0.000000000 1.302775638 + 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:

| 3x+26=5x-8 | | 9k*9k/3k= | | 8w=3840 | | 9k2/3k= | | 5(x)=2(x-3) | | 5(s+3)+2=7 | | 1+4+3+9= | | 4w*5w= | | P-1/2 | | 9x-20=7x+5 | | Tanx-5=0 | | 7x-11=6x+9 | | 27y^2-6y-5=0 | | 5(2x+1)=12-5 | | 3x*5x=60 | | 3(3x+3)=3(4x-1) | | -1/2=4/7u-4/3= | | 5p-1=17 | | 2y+5=3-3y | | 40=-5/12x | | 8x+24=40 | | 7x+17=9x+19 | | 3x+4y-x+3y= | | 3(a+2)=63 | | 15x-30=2x+6 | | x^4-16x^2-100=0 | | -48=6(x-3) | | 2A^2+3a=90 | | -30=5(x-9) | | 7/m+9=m+10 | | 3(x-4)=8(4x-9) | | x^2+2xy+y^2=81 |

Equations solver categories