x^4-32x^2=114

Simple and best practice solution for x^4-32x^2=114 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^4-32x^2=114 equation: 


Simplifying
x4 + -32x2 = 114

Reorder the terms:
-32x2 + x4 = 114

Solving
-32x2 + x4 = 114

Solving for variable 'x'.

Reorder the terms:
-114 + -32x2 + x4 = 114 + -114

Combine like terms: 114 + -114 = 0
-114 + -32x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '114' to each side of the equation.
-114 + -32x2 + 114 + x4 = 0 + 114

Reorder the terms:
-114 + 114 + -32x2 + x4 = 0 + 114

Combine like terms: -114 + 114 = 0
0 + -32x2 + x4 = 0 + 114
-32x2 + x4 = 0 + 114

Combine like terms: 0 + 114 = 114
-32x2 + x4 = 114

The x term is -32x2.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x2 + 256 + x4 = 114 + 256

Reorder the terms:
256 + -32x2 + x4 = 114 + 256

Combine like terms: 114 + 256 = 370
256 + -32x2 + x4 = 370

Factor a perfect square on the left side:
(x2 + -16)(x2 + -16) = 370

Calculate the square root of the right side: 19.235384062

Break this problem into two subproblems by setting 
(x2 + -16) equal to 19.235384062 and -19.235384062.


Subproblem 1
x2 + -16 = 19.235384062

Simplifying
x2 + -16 = 19.235384062

Reorder the terms:
-16 + x2 = 19.235384062

Solving
-16 + x2 = 19.235384062

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x2 = 19.235384062 + 16

Combine like terms: -16 + 16 = 0
0 + x2 = 19.235384062 + 16
x2 = 19.235384062 + 16

Combine like terms: 19.235384062 + 16 = 35.235384062
x2 = 35.235384062

Simplifying
x2 = 35.235384062

Take the square root of each side:
x = {-5.935940032, 5.935940032}


Subproblem 2
x2 + -16 = -19.235384062

Simplifying
x2 + -16 = -19.235384062

Reorder the terms:
-16 + x2 = -19.235384062

Solving
-16 + x2 = -19.235384062

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x2 = -19.235384062 + 16

Combine like terms: -16 + 16 = 0
0 + x2 = -19.235384062 + 16
x2 = -19.235384062 + 16

Combine like terms: -19.235384062 + 16 = -3.235384062
x2 = -3.235384062

Simplifying
x2 = -3.235384062

Reorder the terms:
3.235384062 + x2 = -3.235384062 + 3.235384062

Combine like terms: -3.235384062 + 3.235384062 = 0.000000000
3.235384062 + 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:

| q-18-5=20 | | -7+4=39 | | 4x^5-2x^4+30x^3-15x^2+50x-25=0 | | 5x-9=-14 | | 8y-5=5(y+7)+3y | | 7m-2m=15 | | 6m+5=1 | | (14-2x)x=144 | | 2x^2+2y^2-4x+16y+2=0 | | 4x-10=-58 | | 8(y+2)=32 | | x=-y+4 | | N-3=7 | | 21+11t=-1 | | (14-2x)2x=144 | | 2n+4=6 | | 3+4t=15 | | x+57=73 | | 2w+9=-17 | | -2x+9=7 | | (7.5-y)+0=7.5-y | | 2t+9=-17 | | 4(6-n)-3(8n+9)=12 | | 2(x-5)=4x-2(x+5)+1 | | -7+(x+3)=(x+3)+(-7) | | -5x+7=67 | | 5x^2+1x-22=0 | | 8p+3p-9=16p+3+3p | | -4+u=-16 | | mx+4y=3c | | 4x-5=-37 | | 4(y+2)=16 |

Equations solver categories