x^4=8-x^2

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


Simplifying
x4 = 8 + -1x2

Solving
x4 = 8 + -1x2

Solving for variable 'x'.

Reorder the terms:
-8 + x2 + x4 = 8 + -1x2 + -8 + x2

Reorder the terms:
-8 + x2 + x4 = 8 + -8 + -1x2 + x2

Combine like terms: 8 + -8 = 0
-8 + x2 + x4 = 0 + -1x2 + x2
-8 + x2 + x4 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-8 + x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x2.  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.
x2 + 0.25 + x4 = 8 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + x2 + x4 = 8.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

x2 + 0.5 = 2.872281323 Simplifying x2 + 0.5 = 2.872281323 Reorder the terms: 0.5 + x2 = 2.872281323 Solving 0.5 + x2 = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 2.872281323 + -0.5 x2 = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 x2 = 2.372281323 Simplifying x2 = 2.372281323 Take the square root of each side: x = {-1.540221193, 1.540221193}

Subproblem 2

x2 + 0.5 = -2.872281323 Simplifying x2 + 0.5 = -2.872281323 Reorder the terms: 0.5 + x2 = -2.872281323 Solving 0.5 + x2 = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -2.872281323 + -0.5 x2 = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 x2 = -3.372281323 Simplifying x2 = -3.372281323 Reorder the terms: 3.372281323 + x2 = -3.372281323 + 3.372281323 Combine like terms: -3.372281323 + 3.372281323 = 0.000000000 3.372281323 + 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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