k^4-7k^2=12

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Solution for k^4-7k^2=12 equation: 


Simplifying
k4 + -7k2 = 12

Reorder the terms:
-7k2 + k4 = 12

Solving
-7k2 + k4 = 12

Solving for variable 'k'.

Reorder the terms:
-12 + -7k2 + k4 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -7k2 + k4 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -7k2 + 12 + k4 = 0 + 12

Reorder the terms:
-12 + 12 + -7k2 + k4 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -7k2 + k4 = 0 + 12
-7k2 + k4 = 0 + 12

Combine like terms: 0 + 12 = 12
-7k2 + k4 = 12

The k term is -7k2.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7k2 + 12.25 + k4 = 12 + 12.25

Reorder the terms:
12.25 + -7k2 + k4 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + -7k2 + k4 = 24.25

Factor a perfect square on the left side:
(k2 + -3.5)(k2 + -3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(k2 + -3.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
k2 + -3.5 = 4.924428901

Simplifying
k2 + -3.5 = 4.924428901

Reorder the terms:
-3.5 + k2 = 4.924428901

Solving
-3.5 + k2 = 4.924428901

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k2 = 4.924428901 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k2 = 4.924428901 + 3.5
k2 = 4.924428901 + 3.5

Combine like terms: 4.924428901 + 3.5 = 8.424428901
k2 = 8.424428901

Simplifying
k2 = 8.424428901

Take the square root of each side:
k = {-2.902486675, 2.902486675}


Subproblem 2
k2 + -3.5 = -4.924428901

Simplifying
k2 + -3.5 = -4.924428901

Reorder the terms:
-3.5 + k2 = -4.924428901

Solving
-3.5 + k2 = -4.924428901

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k2 = -4.924428901 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k2 = -4.924428901 + 3.5
k2 = -4.924428901 + 3.5

Combine like terms: -4.924428901 + 3.5 = -1.424428901
k2 = -1.424428901

Simplifying
k2 = -1.424428901

Reorder the terms:
1.424428901 + k2 = -1.424428901 + 1.424428901

Combine like terms: -1.424428901 + 1.424428901 = 0.000000000
1.424428901 + k2 = 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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