x^4-16x^2+32=0

Simple and best practice solution for x^4-16x^2+32=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^4-16x^2+32=0 equation:


Simplifying
x4 + -16x2 + 32 = 0

Reorder the terms:
32 + -16x2 + x4 = 0

Solving
32 + -16x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -16x2 + -32 + x4 = 0 + -32

Reorder the terms:
32 + -32 + -16x2 + x4 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -16x2 + x4 = 0 + -32
-16x2 + x4 = 0 + -32

Combine like terms: 0 + -32 = -32
-16x2 + x4 = -32

The x term is -16x2.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x2 + 64 + x4 = -32 + 64

Reorder the terms:
64 + -16x2 + x4 = -32 + 64

Combine like terms: -32 + 64 = 32
64 + -16x2 + x4 = 32

Factor a perfect square on the left side:
(x2 + -8)(x2 + -8) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x2 + -8) equal to 5.656854249 and -5.656854249.

Subproblem 1

x2 + -8 = 5.656854249 Simplifying x2 + -8 = 5.656854249 Reorder the terms: -8 + x2 = 5.656854249 Solving -8 + x2 = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 5.656854249 + 8 x2 = 5.656854249 + 8 Combine like terms: 5.656854249 + 8 = 13.656854249 x2 = 13.656854249 Simplifying x2 = 13.656854249 Take the square root of each side: x = {-3.69551813, 3.69551813}

Subproblem 2

x2 + -8 = -5.656854249 Simplifying x2 + -8 = -5.656854249 Reorder the terms: -8 + x2 = -5.656854249 Solving -8 + x2 = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -5.656854249 + 8 x2 = -5.656854249 + 8 Combine like terms: -5.656854249 + 8 = 2.343145751 x2 = 2.343145751 Simplifying x2 = 2.343145751 Take the square root of each side: x = {-1.53073373, 1.53073373}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.69551813, 3.69551813, -1.53073373, 1.53073373}

See similar equations:

| -1-6(-8z+8)=-8(-5z+7)+3 | | y=3t^2-16t+2 | | 45+6=78 | | y=-3/4+2 | | 1.5y+5.2=-1.8y-1.4 | | -4.9=-5.4+8.4 | | -15w+30=3(-5w+10) | | 9y-6x=11 | | 3(3+2x)=(21) | | x+2y=0.7 | | 7x+8y=8 | | 2(x+2)=-4(5+4x)+18x | | 9x-25+3x+72=-13 | | 2/3*3/5= | | 8-6(6)=32 | | -0.3(a-0.5)=0.2(a-6) | | 8-6(2)=32 | | 1/2+1/4-1/3= | | 18y=8y | | 1+7x=3-x | | 8-6(-7)=32 | | 2(2+1)=94 | | 1.5x^2=4.75x-2.3 | | 2+1=94 | | 3(-3)-2= | | 1.5x^2=5.5x-2.2 | | 1.3+3.1x=x+25.8 | | x+2y=8.5 | | 3-4x+2x+7-6=10 | | y=12x^2-13x-14 | | 3(4z+8)=-6z-48 | | 6(x-4)-5x=-3(x+8)+4x |

Equations solver categories