4x^4-100x^2-1=0

Simple and best practice solution for 4x^4-100x^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 4x^4-100x^2-1=0 equation: 


Simplifying
4x4 + -100x2 + -1 = 0

Reorder the terms:
-1 + -100x2 + 4x4 = 0

Solving
-1 + -100x2 + 4x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-0.25 + -25x2 + x4 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -25x2 + 0.25 + x4 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -25x2 + x4 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -25x2 + x4 = 0 + 0.25
-25x2 + x4 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-25x2 + x4 = 0.25

The x term is -25x2.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x2 + 156.25 + x4 = 0.25 + 156.25

Reorder the terms:
156.25 + -25x2 + x4 = 0.25 + 156.25

Combine like terms: 0.25 + 156.25 = 156.5
156.25 + -25x2 + x4 = 156.5

Factor a perfect square on the left side:
(x2 + -12.5)(x2 + -12.5) = 156.5

Calculate the square root of the right side: 12.509996003

Break this problem into two subproblems by setting 
(x2 + -12.5) equal to 12.509996003 and -12.509996003.


Subproblem 1
x2 + -12.5 = 12.509996003

Simplifying
x2 + -12.5 = 12.509996003

Reorder the terms:
-12.5 + x2 = 12.509996003

Solving
-12.5 + x2 = 12.509996003

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x2 = 12.509996003 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x2 = 12.509996003 + 12.5
x2 = 12.509996003 + 12.5

Combine like terms: 12.509996003 + 12.5 = 25.009996003
x2 = 25.009996003

Simplifying
x2 = 25.009996003

Take the square root of each side:
x = {-5.0009995, 5.0009995}


Subproblem 2
x2 + -12.5 = -12.509996003

Simplifying
x2 + -12.5 = -12.509996003

Reorder the terms:
-12.5 + x2 = -12.509996003

Solving
-12.5 + x2 = -12.509996003

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x2 = -12.509996003 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x2 = -12.509996003 + 12.5
x2 = -12.509996003 + 12.5

Combine like terms: -12.509996003 + 12.5 = -0.009996003
x2 = -0.009996003

Simplifying
x2 = -0.009996003

Reorder the terms:
0.009996003 + x2 = -0.009996003 + 0.009996003

Combine like terms: -0.009996003 + 0.009996003 = 0.000000000
0.009996003 + 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:

| Y=x^4-4x^2 | | 8xy-3x=w | | -7x-2(3x+13)=-182 | | 32+6x=-40 | | 0=-3(y-5) | | 4n-6m=-12 | | a+2(9+1)=10 | | 15x+3=19x-5 | | m-3n=7 | | 20x17/20 | | 400x=920 | | 6y+8=4(y-10) | | 5x-6=6x-9 | | 18x-5=16x+5 | | y^2+7y-4=0 | | -9(t+4)=9 | | 0.1x^3-2x-7992=0 | | Y-6=2(x+5) | | a+2(a+5)=-4(a+1) | | f(x)=3xln(9x^4-3x+2) | | -(2x-4)=-3x+6 | | -66=-6x+2(-6x+12) | | 8y(3y-2z)= | | 6W+8=4 | | -(2x-4)=-3x | | 6.5c+12=-1 | | -12t+-60=-60 | | 7=2x-28 | | x+12+8x-21=180 | | -3y+23=6y-4 | | n+60=94 | | 8(x^3)-40x=0 |

Equations solver categories