k^4=8-7k^2

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Solution for k^4=8-7k^2 equation: 


Simplifying
k4 = 8 + -7k2

Solving
k4 = 8 + -7k2

Solving for variable 'k'.

Reorder the terms:
-8 + 7k2 + k4 = 8 + -7k2 + -8 + 7k2

Reorder the terms:
-8 + 7k2 + k4 = 8 + -8 + -7k2 + 7k2

Combine like terms: 8 + -8 = 0
-8 + 7k2 + k4 = 0 + -7k2 + 7k2
-8 + 7k2 + k4 = -7k2 + 7k2

Combine like terms: -7k2 + 7k2 = 0
-8 + 7k2 + k4 = 0

Factor a trinomial.
(-8 + -1k2)(1 + -1k2) = 0

Factor a difference between two squares.
(-8 + -1k2)((1 + k)(1 + -1k)) = 0


Subproblem 1
Set the factor '(-8 + -1k2)' equal to zero and attempt to solve:

Simplifying
-8 + -1k2 = 0

Solving
-8 + -1k2 = 0

Move all terms containing k to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1k2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1k2 = 0 + 8
-1k2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1k2 = 8

Divide each side by '-1'.
k2 = -8

Simplifying
k2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

Solving
1 + k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + k = 0 + -1
k = 0 + -1

Combine like terms: 0 + -1 = -1
k = -1

Simplifying
k = -1

Subproblem 3
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1k = 0 + -1
-1k = 0 + -1

Combine like terms: 0 + -1 = -1
-1k = -1

Divide each side by '-1'.
k = 1

Simplifying
k = 1
Solution
k = {-1, 1}

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