3x^4-16x^2-225=0

Simple and best practice solution for 3x^4-16x^2-225=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 3x^4-16x^2-225=0 equation: 


Simplifying
3x4 + -16x2 + -225 = 0

Reorder the terms:
-225 + -16x2 + 3x4 = 0

Solving
-225 + -16x2 + 3x4 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-75 + -5.333333333x2 + x4 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -5.333333333x2 + 75 + x4 = 0 + 75

Reorder the terms:
-75 + 75 + -5.333333333x2 + x4 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -5.333333333x2 + x4 = 0 + 75
-5.333333333x2 + x4 = 0 + 75

Combine like terms: 0 + 75 = 75
-5.333333333x2 + x4 = 75

The x term is -5.333333333x2.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x2 + 7.111111113 + x4 = 75 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x2 + x4 = 75 + 7.111111113

Combine like terms: 75 + 7.111111113 = 82.111111113
7.111111113 + -5.333333333x2 + x4 = 82.111111113

Factor a perfect square on the left side:
(x2 + -2.666666667)(x2 + -2.666666667) = 82.111111113

Calculate the square root of the right side: 9.061518146

Break this problem into two subproblems by setting 
(x2 + -2.666666667) equal to 9.061518146 and -9.061518146.


Subproblem 1
x2 + -2.666666667 = 9.061518146

Simplifying
x2 + -2.666666667 = 9.061518146

Reorder the terms:
-2.666666667 + x2 = 9.061518146

Solving
-2.666666667 + x2 = 9.061518146

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x2 = 9.061518146 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x2 = 9.061518146 + 2.666666667
x2 = 9.061518146 + 2.666666667

Combine like terms: 9.061518146 + 2.666666667 = 11.728184813
x2 = 11.728184813

Simplifying
x2 = 11.728184813

Take the square root of each side:
x = {-3.42464375, 3.42464375}


Subproblem 2
x2 + -2.666666667 = -9.061518146

Simplifying
x2 + -2.666666667 = -9.061518146

Reorder the terms:
-2.666666667 + x2 = -9.061518146

Solving
-2.666666667 + x2 = -9.061518146

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x2 = -9.061518146 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x2 = -9.061518146 + 2.666666667
x2 = -9.061518146 + 2.666666667

Combine like terms: -9.061518146 + 2.666666667 = -6.394851479
x2 = -6.394851479

Simplifying
x2 = -6.394851479

Reorder the terms:
6.394851479 + x2 = -6.394851479 + 6.394851479

Combine like terms: -6.394851479 + 6.394851479 = 0.000000000
6.394851479 + 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:

| f(x)=(1.93)x | | 9.25=logx | | 3(x-5)-4(2x-6)=6(x+4) | | x+(x+100)+x=1850 | | 4(x-2)=3(3+x) | | 25x+35y=180 | | 6x+2=5x-27+3x+1 | | 2x+x=64 | | -6x=132 | | 4(x-3)=2(2-x) | | 4(x-2)-5(2x-3)=3(x+4) | | 3(x-2)+4(x-3)=6(x-5) | | 2/10=2/100 | | 100+38x=C | | r=st | | 7s+1=12+7s | | f(x)=3-32x | | (x)(2x+3)=324 | | X(x-2a)+a^2-1=0 | | 5c-4c+c-3= | | 3a+6+5a-3= | | 2x^2+28x+16=0 | | 5x-5+4x+7= | | y/2+3=7 | | x-5/6=2/14 | | 5x^2-60x+180= | | 9x^4y^2-z^6= | | 2/3x+10=-2 | | 2(2x-1)+2=3x-4 | | 7x+4-1=3 | | 3x-(5-x)=3(4/3x-1) | | 25.12*4/3 |

Equations solver categories