x^4-36x^2+81=0

Simple and best practice solution for x^4-36x^2+81=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^4-36x^2+81=0 equation: 


Simplifying
x4 + -36x2 + 81 = 0

Reorder the terms:
81 + -36x2 + x4 = 0

Solving
81 + -36x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + -36x2 + -81 + x4 = 0 + -81

Reorder the terms:
81 + -81 + -36x2 + x4 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -36x2 + x4 = 0 + -81
-36x2 + x4 = 0 + -81

Combine like terms: 0 + -81 = -81
-36x2 + x4 = -81

The x term is -36x2.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x2 + 324 + x4 = -81 + 324

Reorder the terms:
324 + -36x2 + x4 = -81 + 324

Combine like terms: -81 + 324 = 243
324 + -36x2 + x4 = 243

Factor a perfect square on the left side:
(x2 + -18)(x2 + -18) = 243

Calculate the square root of the right side: 15.588457268

Break this problem into two subproblems by setting 
(x2 + -18) equal to 15.588457268 and -15.588457268.


Subproblem 1
x2 + -18 = 15.588457268

Simplifying
x2 + -18 = 15.588457268

Reorder the terms:
-18 + x2 = 15.588457268

Solving
-18 + x2 = 15.588457268

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x2 = 15.588457268 + 18

Combine like terms: -18 + 18 = 0
0 + x2 = 15.588457268 + 18
x2 = 15.588457268 + 18

Combine like terms: 15.588457268 + 18 = 33.588457268
x2 = 33.588457268

Simplifying
x2 = 33.588457268

Take the square root of each side:
x = {-5.795554958, 5.795554958}


Subproblem 2
x2 + -18 = -15.588457268

Simplifying
x2 + -18 = -15.588457268

Reorder the terms:
-18 + x2 = -15.588457268

Solving
-18 + x2 = -15.588457268

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x2 = -15.588457268 + 18

Combine like terms: -18 + 18 = 0
0 + x2 = -15.588457268 + 18
x2 = -15.588457268 + 18

Combine like terms: -15.588457268 + 18 = 2.411542732
x2 = 2.411542732

Simplifying
x2 = 2.411542732

Take the square root of each side:
x = {-1.552914271, 1.552914271}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.795554958, 5.795554958, -1.552914271, 1.552914271}

See similar equations:

| (14+2p)+(20+2n)+p=12 | | -4(x+2)=32 | | 4z+9-z=1+2z+2 | | -302/x=-75.5 | | -1208/x=-302 | | x^4-36x^2+21.7=0 | | x^4-35x^2+21.7=0 | | 7=5y-4y+2 | | 5m+12=28 | | 10y+11x=230 | | 66.6x-4=-16 | | 2-1.7= | | 7x+9y=178 | | (a^3b^4+a^2b^2)+(a^2b^2-a^3b^4)= | | x^4-36x^2+243=0 | | 8y+10=65 | | x^4+36x^2-1944=0 | | 5(3/4x-1)=2x | | =7tanx | | 1-2*(-3)+(-7)-3x=-9 | | 4x+-2y=15 | | 12-x+(-7)+5*5=-1 | | -313+-172x+-2x^2+3x^3=0 | | 3x^3-2x^2-172x-312=1 | | 3x^2-20x-11=0 | | 2a-3*(-2)+4=0 | | 1x^2-1x-20=0 | | 3x-6-2*(-1)=2 | | 3t^2-11t-20=0 | | .3-1.2v=3.2 | | 2x^3=-8x^2 | | x^2+16x+78=0 |

Equations solver categories