k^4-k^2=11

Simple and best practice solution for k^4-k^2=11 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for k^4-k^2=11 equation: 


Simplifying
k4 + -1k2 = 11

Reorder the terms:
-1k2 + k4 = 11

Solving
-1k2 + k4 = 11

Solving for variable 'k'.

Reorder the terms:
-11 + -1k2 + k4 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -1k2 + k4 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -1k2 + 11 + k4 = 0 + 11

Reorder the terms:
-11 + 11 + -1k2 + k4 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1k2 + k4 = 0 + 11
-1k2 + k4 = 0 + 11

Combine like terms: 0 + 11 = 11
-1k2 + k4 = 11

The k term is -1k2.  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.
-1k2 + 0.25 + k4 = 11 + 0.25

Reorder the terms:
0.25 + -1k2 + k4 = 11 + 0.25

Combine like terms: 11 + 0.25 = 11.25
0.25 + -1k2 + k4 = 11.25

Factor a perfect square on the left side:
(k2 + -0.5)(k2 + -0.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(k2 + -0.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
k2 + -0.5 = 3.354101966

Simplifying
k2 + -0.5 = 3.354101966

Reorder the terms:
-0.5 + k2 = 3.354101966

Solving
-0.5 + k2 = 3.354101966

Solving for variable 'k'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + k2 = 3.354101966 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k2 = 3.354101966 + 0.5
k2 = 3.354101966 + 0.5

Combine like terms: 3.354101966 + 0.5 = 3.854101966
k2 = 3.854101966

Simplifying
k2 = 3.854101966

Take the square root of each side:
k = {-1.963186686, 1.963186686}


Subproblem 2
k2 + -0.5 = -3.354101966

Simplifying
k2 + -0.5 = -3.354101966

Reorder the terms:
-0.5 + k2 = -3.354101966

Solving
-0.5 + k2 = -3.354101966

Solving for variable 'k'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + k2 = -3.354101966 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k2 = -3.354101966 + 0.5
k2 = -3.354101966 + 0.5

Combine like terms: -3.354101966 + 0.5 = -2.854101966
k2 = -2.854101966

Simplifying
k2 = -2.854101966

Reorder the terms:
2.854101966 + k2 = -2.854101966 + 2.854101966

Combine like terms: -2.854101966 + 2.854101966 = 0.000000000
2.854101966 + 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.

See similar equations:

| 7/8.4/7 | | y=7x+77 | | 15/1.2/3 | | 8x-3=8(x-6) | | 2/3x15/1 | | 7(5x-2)=35x-14 | | (12.93)+2(0.11)= | | (12.93)-2(0.11)= | | -2.1(y-1.5)=0.4(y+16) | | t/5-1=10 | | (x+8)(x-2)(x-1)= | | 8x-9=2x+7+3x^2 | | 4x^2+8x-24=0 | | 2/2x15 | | (80.6)+2(10.3)= | | (80.6)-2(10.3)= | | ln(1+x)=5 | | (x+37)+90+(x+67)=180 | | 10a+bfora= | | 20x+10y=30 | | -414=99x+22y | | d÷15/4=4/3 | | (12.63)+2(0.12)= | | (12.63)-2(0.12)= | | 0.6666666667(5-a)=2 | | P=3a+4ab | | n/2-7=4 | | 12/15=x/20 | | 0.8(x+10)=-1.3(x+12) | | 7-3c=c-1 | | 99=33+3*(3x+5) | | (70.2)+2(13.1)= |

Equations solver categories