x^4-2x^2-54=0

Simple and best practice solution for x^4-2x^2-54=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^4-2x^2-54=0 equation:


Simplifying
x4 + -2x2 + -54 = 0

Reorder the terms:
-54 + -2x2 + x4 = 0

Solving
-54 + -2x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -2x2 + 54 + x4 = 0 + 54

Reorder the terms:
-54 + 54 + -2x2 + x4 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -2x2 + x4 = 0 + 54
-2x2 + x4 = 0 + 54

Combine like terms: 0 + 54 = 54
-2x2 + x4 = 54

The x term is -2x2.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x2 + 1 + x4 = 54 + 1

Reorder the terms:
1 + -2x2 + x4 = 54 + 1

Combine like terms: 54 + 1 = 55
1 + -2x2 + x4 = 55

Factor a perfect square on the left side:
(x2 + -1)(x2 + -1) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x2 + -1) equal to 7.416198487 and -7.416198487.

Subproblem 1

x2 + -1 = 7.416198487 Simplifying x2 + -1 = 7.416198487 Reorder the terms: -1 + x2 = 7.416198487 Solving -1 + x2 = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 7.416198487 + 1 x2 = 7.416198487 + 1 Combine like terms: 7.416198487 + 1 = 8.416198487 x2 = 8.416198487 Simplifying x2 = 8.416198487 Take the square root of each side: x = {-2.901068508, 2.901068508}

Subproblem 2

x2 + -1 = -7.416198487 Simplifying x2 + -1 = -7.416198487 Reorder the terms: -1 + x2 = -7.416198487 Solving -1 + x2 = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -7.416198487 + 1 x2 = -7.416198487 + 1 Combine like terms: -7.416198487 + 1 = -6.416198487 x2 = -6.416198487 Simplifying x2 = -6.416198487 Reorder the terms: 6.416198487 + x2 = -6.416198487 + 6.416198487 Combine like terms: -6.416198487 + 6.416198487 = 0.000000000 6.416198487 + 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:

| x-2.5=0 | | 9(5x+3)=342 | | 2(1x+4)+6=22 | | 8x+5y+2.2=6x+7y | | 6.28+8.64= | | 8.64+6.15= | | m^2-32=4m | | 10x-9=9x+10 | | -3(x-3)+2(3x-2)=14 | | 0.1y^2=10 | | 2.5+6.4= | | T-t=20 | | log(6x-7)-log(x-5)=1 | | 3y^2+6y-35=0 | | 2.8+6.1= | | logx=.3344 | | 9.75=3.5k | | -4(8n-2)=104 | | 5.3+6.4= | | a+20=2a-50 | | 1.2+2.6= | | 4.5g=9 | | 9(r-7)= | | 9y+45=6x | | a+5b-a-b=x | | 1-7(1-6a)=-258 | | -12n+15=-11n-17 | | (4x-2)*6(2x+7)=0 | | 1.0r=50 | | -14g+19g=-15 | | 175=-7(7x-4) | | 34-14= |

Equations solver categories