x^4-x^2-391=0

Simple and best practice solution for x^4-x^2-391=0 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 x^4-x^2-391=0 equation: 


Simplifying
x4 + -1x2 + -391 = 0

Reorder the terms:
-391 + -1x2 + x4 = 0

Solving
-391 + -1x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '391' to each side of the equation.
-391 + -1x2 + 391 + x4 = 0 + 391

Reorder the terms:
-391 + 391 + -1x2 + x4 = 0 + 391

Combine like terms: -391 + 391 = 0
0 + -1x2 + x4 = 0 + 391
-1x2 + x4 = 0 + 391

Combine like terms: 0 + 391 = 391
-1x2 + x4 = 391

The x term is -1x2.  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.
-1x2 + 0.25 + x4 = 391 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 391 + 0.25

Combine like terms: 391 + 0.25 = 391.25
0.25 + -1x2 + x4 = 391.25

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 391.25

Calculate the square root of the right side: 19.780040445

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 19.780040445 and -19.780040445.


Subproblem 1
x2 + -0.5 = 19.780040445

Simplifying
x2 + -0.5 = 19.780040445

Reorder the terms:
-0.5 + x2 = 19.780040445

Solving
-0.5 + x2 = 19.780040445

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 = 19.780040445 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 19.780040445 + 0.5
x2 = 19.780040445 + 0.5

Combine like terms: 19.780040445 + 0.5 = 20.280040445
x2 = 20.280040445

Simplifying
x2 = 20.280040445

Take the square root of each side:
x = {-4.50333659, 4.50333659}


Subproblem 2
x2 + -0.5 = -19.780040445

Simplifying
x2 + -0.5 = -19.780040445

Reorder the terms:
-0.5 + x2 = -19.780040445

Solving
-0.5 + x2 = -19.780040445

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 = -19.780040445 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -19.780040445 + 0.5
x2 = -19.780040445 + 0.5

Combine like terms: -19.780040445 + 0.5 = -19.280040445
x2 = -19.280040445

Simplifying
x2 = -19.280040445

Reorder the terms:
19.280040445 + x2 = -19.280040445 + 19.280040445

Combine like terms: -19.280040445 + 19.280040445 = 0.000000000
19.280040445 + 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.

See similar equations:

| 4x+x=-35-2x | | (2+3i)-(7+5i)=0 | | 5x-40=x-8 | | (2x-3)-(4x+1)= | | 10a+6=5a-9 | | 0.3x=1.2+2.3x | | -3-2(5x-7)=-12 | | x^2+5-50=0 | | 0.06(y-4)+0.14y=0.16y-0.01(30) | | 4-3x/2=5 | | 3+x+3+8=92 | | 8-6(2x-1)=40 | | -4-7=31 | | 1/3r=1+1/r | | C-14=-23 | | t^4-4t^3+5t^2+2t-12=0 | | -6(2t+1)=-66 | | 5x+y-3=0 | | 4x+11=201 | | 12+8-4x=-20 | | x+3+8=92 | | 3(2x-1)-5x+2=11-8(x+3) | | 4(f-6)=12 | | 5/8/t=95 | | V^2-4v-16=0 | | 4-(7/6x)8 | | 10(s-6)=-118 | | 3y^2-7y+4y^2-2y= | | f(1)=1 | | 6x+15y=9 | | 2(n+1/3)=3/2n+1 | | 74-2x=7x+24 |

Equations solver categories