x^4-32x^2+1=0

Simple and best practice solution for x^4-32x^2+1=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+1=0 equation:


Simplifying
x4 + -32x2 + 1 = 0

Reorder the terms:
1 + -32x2 + x4 = 0

Solving
1 + -32x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -32x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + -32x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -32x2 + x4 = 0 + -1
-32x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-32x2 + x4 = -1

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 = -1 + 256

Reorder the terms:
256 + -32x2 + x4 = -1 + 256

Combine like terms: -1 + 256 = 255
256 + -32x2 + x4 = 255

Factor a perfect square on the left side:
(x2 + -16)(x2 + -16) = 255

Calculate the square root of the right side: 15.968719423

Break this problem into two subproblems by setting 
(x2 + -16) equal to 15.968719423 and -15.968719423.

Subproblem 1

x2 + -16 = 15.968719423 Simplifying x2 + -16 = 15.968719423 Reorder the terms: -16 + x2 = 15.968719423 Solving -16 + x2 = 15.968719423 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 = 15.968719423 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = 15.968719423 + 16 x2 = 15.968719423 + 16 Combine like terms: 15.968719423 + 16 = 31.968719423 x2 = 31.968719423 Simplifying x2 = 31.968719423 Take the square root of each side: x = {-5.654088735, 5.654088735}

Subproblem 2

x2 + -16 = -15.968719423 Simplifying x2 + -16 = -15.968719423 Reorder the terms: -16 + x2 = -15.968719423 Solving -16 + x2 = -15.968719423 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 = -15.968719423 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = -15.968719423 + 16 x2 = -15.968719423 + 16 Combine like terms: -15.968719423 + 16 = 0.031280577 x2 = 0.031280577 Simplifying x2 = 0.031280577 Take the square root of each side: x = {-0.176863159, 0.176863159}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.654088735, 5.654088735, -0.176863159, 0.176863159}

See similar equations:

| yx-6+10=7 | | 45=-9/5x | | 7x+20x=16x | | 7x-5=-8x+25 | | 5(x+7)-3x=2(x-5)+4 | | 6x+8-4x=7x+9 | | 6(7x+1)=42x+6 | | 5-7(x+1)=2 | | 2w+3w=30 | | -50x-(-50)=0 | | 4a-5b/6a/7b | | 5-7(x+1)=1 | | x+2.5=6.8 | | x^3-12x-38=0 | | 0.06(y-4)+0.04y=0.02y-0.7 | | 27-2x-7=3x-x | | 27-2x-7=3x-3 | | 8=1.5+b | | 3=8+b | | -6=3x/7 | | 9-(2z-4)=9-3z | | y=(x^2+9) | | 8/1x5/7 | | (-54+-9x)=14 | | 6q+3(1-q)=3q+8(1-q) | | 8x5/7 | | 6(z-8)=3+7z | | 9x=9-9x | | 6y+(2y-3)=13 | | sin(2x)=2cos^2(x) | | 4(x+1)=2(3x-2) | | 11/x=21/35 |

Equations solver categories