x^4-32x^2+64=0

Simple and best practice solution for x^4-32x^2+64=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^4-32x^2+64=0 equation:


Simplifying
x4 + -32x2 + 64 = 0

Reorder the terms:
64 + -32x2 + x4 = 0

Solving
64 + -32x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -32x2 + -64 + x4 = 0 + -64

Reorder the terms:
64 + -64 + -32x2 + x4 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -32x2 + x4 = 0 + -64
-32x2 + x4 = 0 + -64

Combine like terms: 0 + -64 = -64
-32x2 + x4 = -64

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 = -64 + 256

Reorder the terms:
256 + -32x2 + x4 = -64 + 256

Combine like terms: -64 + 256 = 192
256 + -32x2 + x4 = 192

Factor a perfect square on the left side:
(x2 + -16)(x2 + -16) = 192

Calculate the square root of the right side: 13.856406461

Break this problem into two subproblems by setting 
(x2 + -16) equal to 13.856406461 and -13.856406461.

Subproblem 1

x2 + -16 = 13.856406461 Simplifying x2 + -16 = 13.856406461 Reorder the terms: -16 + x2 = 13.856406461 Solving -16 + x2 = 13.856406461 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 = 13.856406461 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = 13.856406461 + 16 x2 = 13.856406461 + 16 Combine like terms: 13.856406461 + 16 = 29.856406461 x2 = 29.856406461 Simplifying x2 = 29.856406461 Take the square root of each side: x = {-5.464101615, 5.464101615}

Subproblem 2

x2 + -16 = -13.856406461 Simplifying x2 + -16 = -13.856406461 Reorder the terms: -16 + x2 = -13.856406461 Solving -16 + x2 = -13.856406461 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 = -13.856406461 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = -13.856406461 + 16 x2 = -13.856406461 + 16 Combine like terms: -13.856406461 + 16 = 2.143593539 x2 = 2.143593539 Simplifying x2 = 2.143593539 Take the square root of each side: x = {-1.464101615, 1.464101615}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.464101615, 5.464101615, -1.464101615, 1.464101615}

See similar equations:

| (12+h)(h-3)=324 | | -7(2+8)= | | x^4-72x^2+144=0 | | 6(3*2-1)= | | log[7](1+3x)=log[7]2 | | 9n/37=27/296 | | 10x+5y+3z=21 | | 1/2x^2-3/2x-2 | | X/3-x/7=4 | | 9x-y+4z=37 | | -b+6= | | sin(25x)+sin(5x)=0 | | 0=4x^2-13x+9 | | 3-4x/5=4=x/5 | | 15/8x=-195/32 | | x+22+3x=-4-3x-9 | | (x)(5+x)=84 | | -4.5=-0.5(x-7.1) | | 2s-1458/s^2=0 | | 4(t+0.25)=3 | | 105x-16x^2=34 | | 105x-16x^2=0 | | 6(1-3m)=8(-2m+5)-4 | | 1.1=0.50+0.03n-0.03 | | 3=-11-n | | -3p+8=5-9p-4 | | 10x+6xln*(x^2)=0 | | f(x)=5ln(5x) | | 5^-1x^0/y^-1 | | 4m^2-25/16 | | 4x-18=46 | | 10x=1-(-19) |

Equations solver categories