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

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


Simplifying
x4 + -11x2 + -8 = 0

Reorder the terms:
-8 + -11x2 + x4 = 0

Solving
-8 + -11x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -11x2 + 8 + x4 = 0 + 8

Reorder the terms:
-8 + 8 + -11x2 + x4 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -11x2 + x4 = 0 + 8
-11x2 + x4 = 0 + 8

Combine like terms: 0 + 8 = 8
-11x2 + x4 = 8

The x term is -11x2.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x2 + 30.25 + x4 = 8 + 30.25

Reorder the terms:
30.25 + -11x2 + x4 = 8 + 30.25

Combine like terms: 8 + 30.25 = 38.25
30.25 + -11x2 + x4 = 38.25

Factor a perfect square on the left side:
(x2 + -5.5)(x2 + -5.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x2 + -5.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

x2 + -5.5 = 6.184658438 Simplifying x2 + -5.5 = 6.184658438 Reorder the terms: -5.5 + x2 = 6.184658438 Solving -5.5 + x2 = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = 6.184658438 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = 6.184658438 + 5.5 x2 = 6.184658438 + 5.5 Combine like terms: 6.184658438 + 5.5 = 11.684658438 x2 = 11.684658438 Simplifying x2 = 11.684658438 Take the square root of each side: x = {-3.418282966, 3.418282966}

Subproblem 2

x2 + -5.5 = -6.184658438 Simplifying x2 + -5.5 = -6.184658438 Reorder the terms: -5.5 + x2 = -6.184658438 Solving -5.5 + x2 = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = -6.184658438 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = -6.184658438 + 5.5 x2 = -6.184658438 + 5.5 Combine like terms: -6.184658438 + 5.5 = -0.684658438 x2 = -0.684658438 Simplifying x2 = -0.684658438 Reorder the terms: 0.684658438 + x2 = -0.684658438 + 0.684658438 Combine like terms: -0.684658438 + 0.684658438 = 0.000000000 0.684658438 + x2 = 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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