x^4+x^2-21=0

Simple and best practice solution for x^4+x^2-21=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^2-21=0 equation:


Simplifying
x4 + x2 + -21 = 0

Reorder the terms:
-21 + x2 + x4 = 0

Solving
-21 + x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + x2 + 21 + x4 = 0 + 21

Reorder the terms:
-21 + 21 + x2 + x4 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + x2 + x4 = 0 + 21
x2 + x4 = 0 + 21

Combine like terms: 0 + 21 = 21
x2 + x4 = 21

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 = 21 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 21 + 0.25

Combine like terms: 21 + 0.25 = 21.25
0.25 + x2 + x4 = 21.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 4.609772229 and -4.609772229.

Subproblem 1

x2 + 0.5 = 4.609772229 Simplifying x2 + 0.5 = 4.609772229 Reorder the terms: 0.5 + x2 = 4.609772229 Solving 0.5 + x2 = 4.609772229 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 = 4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 4.609772229 + -0.5 x2 = 4.609772229 + -0.5 Combine like terms: 4.609772229 + -0.5 = 4.109772229 x2 = 4.109772229 Simplifying x2 = 4.109772229 Take the square root of each side: x = {-2.027257317, 2.027257317}

Subproblem 2

x2 + 0.5 = -4.609772229 Simplifying x2 + 0.5 = -4.609772229 Reorder the terms: 0.5 + x2 = -4.609772229 Solving 0.5 + x2 = -4.609772229 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 = -4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -4.609772229 + -0.5 x2 = -4.609772229 + -0.5 Combine like terms: -4.609772229 + -0.5 = -5.109772229 x2 = -5.109772229 Simplifying x2 = -5.109772229 Reorder the terms: 5.109772229 + x2 = -5.109772229 + 5.109772229 Combine like terms: -5.109772229 + 5.109772229 = 0.000000000 5.109772229 + 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:

| 15m-19m-4=8 | | 3(x+2)+2=7 | | 8x+14=4x+102 | | 5x-6+2x=-27 | | 9x-2(x-3)=2(x-2)+8 | | 9x+3=5x+7 | | 7y-4(y-6)=3-2(y-6) | | 3x+25=11x-55 | | 5x-9=3-x | | 5x-19=37 | | 5-3z=17 | | ln(x+3)-5=-2 | | ln(x+3)=1 | | 15x-20y-1=0 | | 6x+5x-2x=-19 | | 1.39+2.51= | | 77=e | | 3(4x-5)=2x+8 | | -16t^2+160t+176=0 | | 6+7x=54-x | | a^2+5a=14 | | 7-4(a+2)=9+a | | 5d^2+30d+45=0 | | (7x-1)=(3x-9) | | x^2-121y^2=0 | | 2x+25=11x-75 | | x^2=e | | a^2+14a+49=0 | | 5z-14-z+2=0 | | 8x+1=8+15 | | 83=-5(-3r-1)+3 | | 5x-6(x+2)=7 |

Equations solver categories