x^4+8x^2=1

Simple and best practice solution for x^4+8x^2=1 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+8x^2=1 equation:


Simplifying
x4 + 8x2 = 1

Reorder the terms:
8x2 + x4 = 1

Solving
8x2 + x4 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 8x2 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 8x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 8x2 + 1 + x4 = 0 + 1

Reorder the terms:
-1 + 1 + 8x2 + x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8x2 + x4 = 0 + 1
8x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
8x2 + x4 = 1

The x term is 8x2.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x2 + 16 + x4 = 1 + 16

Reorder the terms:
16 + 8x2 + x4 = 1 + 16

Combine like terms: 1 + 16 = 17
16 + 8x2 + x4 = 17

Factor a perfect square on the left side:
(x2 + 4)(x2 + 4) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x2 + 4) equal to 4.123105626 and -4.123105626.

Subproblem 1

x2 + 4 = 4.123105626 Simplifying x2 + 4 = 4.123105626 Reorder the terms: 4 + x2 = 4.123105626 Solving 4 + x2 = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 4.123105626 + -4 x2 = 4.123105626 + -4 Combine like terms: 4.123105626 + -4 = 0.123105626 x2 = 0.123105626 Simplifying x2 = 0.123105626 Take the square root of each side: x = {-0.350864113, 0.350864113}

Subproblem 2

x2 + 4 = -4.123105626 Simplifying x2 + 4 = -4.123105626 Reorder the terms: 4 + x2 = -4.123105626 Solving 4 + x2 = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -4.123105626 + -4 x2 = -4.123105626 + -4 Combine like terms: -4.123105626 + -4 = -8.123105626 x2 = -8.123105626 Simplifying x2 = -8.123105626 Reorder the terms: 8.123105626 + x2 = -8.123105626 + 8.123105626 Combine like terms: -8.123105626 + 8.123105626 = 0.000000000 8.123105626 + 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:

| 2x-7+3x-6+x=5x+2 | | 4p^2=-144 | | -9x^2+65x-14=0 | | 2/3=11/x | | -4x^2-5x+6= | | -9x^2-73x-8=0 | | 6-3x=31 | | 4-2r=r | | -7/m=1 | | 40y^2-50y=0 | | (9/12)a=7/12 | | (0/12)a=7/12 | | 6/x-4=8/x | | y=(15-2x)(8-2x) | | g^2=-18-9g | | 7-2r+4r-15=3r-5 | | 6x+7-14=6+5x+6x | | 24d^2-6d-30=0 | | 4.8g+5=2.8g+15 | | 45(x+6)=945 | | 0.15-0.4= | | 2x^2+7=31 | | 20-14=2(x-4) | | 2x+6+x=1+x-5 | | 5+2m=-1 | | Y(x-4)=x(y-6) | | 8cos^2(x)+16cos(x)+8=0 | | 5+(6+3)=(5+6)+3 | | -10=-b | | 3×-24/18 | | 16t^2-80t+100=0 | | 6+1-2x+5x=-7 |

Equations solver categories