z^4-8z^2-11=0

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Solution for z^4-8z^2-11=0 equation:


Simplifying
z4 + -8z2 + -11 = 0

Reorder the terms:
-11 + -8z2 + z4 = 0

Solving
-11 + -8z2 + z4 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -8z2 + 11 + z4 = 0 + 11

Reorder the terms:
-11 + 11 + -8z2 + z4 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -8z2 + z4 = 0 + 11
-8z2 + z4 = 0 + 11

Combine like terms: 0 + 11 = 11
-8z2 + z4 = 11

The z term is -8z2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8z2 + 16 + z4 = 11 + 16

Reorder the terms:
16 + -8z2 + z4 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + -8z2 + z4 = 27

Factor a perfect square on the left side:
(z2 + -4)(z2 + -4) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(z2 + -4) equal to 5.196152423 and -5.196152423.

Subproblem 1

z2 + -4 = 5.196152423 Simplifying z2 + -4 = 5.196152423 Reorder the terms: -4 + z2 = 5.196152423 Solving -4 + z2 = 5.196152423 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z2 = 5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + z2 = 5.196152423 + 4 z2 = 5.196152423 + 4 Combine like terms: 5.196152423 + 4 = 9.196152423 z2 = 9.196152423 Simplifying z2 = 9.196152423 Take the square root of each side: z = {-3.032515857, 3.032515857}

Subproblem 2

z2 + -4 = -5.196152423 Simplifying z2 + -4 = -5.196152423 Reorder the terms: -4 + z2 = -5.196152423 Solving -4 + z2 = -5.196152423 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z2 = -5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + z2 = -5.196152423 + 4 z2 = -5.196152423 + 4 Combine like terms: -5.196152423 + 4 = -1.196152423 z2 = -1.196152423 Simplifying z2 = -1.196152423 Reorder the terms: 1.196152423 + z2 = -1.196152423 + 1.196152423 Combine like terms: -1.196152423 + 1.196152423 = 0.000000000 1.196152423 + 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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