z^4+z^2=15

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Solution for z^4+z^2=15 equation:


Simplifying
z4 + z2 = 15

Reorder the terms:
z2 + z4 = 15

Solving
z2 + z4 = 15

Solving for variable 'z'.

Reorder the terms:
-15 + z2 + z4 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + z2 + z4 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + z2 + 15 + z4 = 0 + 15

Reorder the terms:
-15 + 15 + z2 + z4 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + z2 + z4 = 0 + 15
z2 + z4 = 0 + 15

Combine like terms: 0 + 15 = 15
z2 + z4 = 15

The z term is z2.  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.
z2 + 0.25 + z4 = 15 + 0.25

Reorder the terms:
0.25 + z2 + z4 = 15 + 0.25

Combine like terms: 15 + 0.25 = 15.25
0.25 + z2 + z4 = 15.25

Factor a perfect square on the left side:
(z2 + 0.5)(z2 + 0.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(z2 + 0.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

z2 + 0.5 = 3.905124838 Simplifying z2 + 0.5 = 3.905124838 Reorder the terms: 0.5 + z2 = 3.905124838 Solving 0.5 + z2 = 3.905124838 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 = 3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z2 = 3.905124838 + -0.5 z2 = 3.905124838 + -0.5 Combine like terms: 3.905124838 + -0.5 = 3.405124838 z2 = 3.405124838 Simplifying z2 = 3.405124838 Take the square root of each side: z = {-1.845298035, 1.845298035}

Subproblem 2

z2 + 0.5 = -3.905124838 Simplifying z2 + 0.5 = -3.905124838 Reorder the terms: 0.5 + z2 = -3.905124838 Solving 0.5 + z2 = -3.905124838 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 = -3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z2 = -3.905124838 + -0.5 z2 = -3.905124838 + -0.5 Combine like terms: -3.905124838 + -0.5 = -4.405124838 z2 = -4.405124838 Simplifying z2 = -4.405124838 Reorder the terms: 4.405124838 + z2 = -4.405124838 + 4.405124838 Combine like terms: -4.405124838 + 4.405124838 = 0.000000000 4.405124838 + 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.

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