x^4+9x^2-16=0

Simple and best practice solution for x^4+9x^2-16=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+9x^2-16=0 equation:


Simplifying
x4 + 9x2 + -16 = 0

Reorder the terms:
-16 + 9x2 + x4 = 0

Solving
-16 + 9x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 9x2 + 16 + x4 = 0 + 16

Reorder the terms:
-16 + 16 + 9x2 + x4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 9x2 + x4 = 0 + 16
9x2 + x4 = 0 + 16

Combine like terms: 0 + 16 = 16
9x2 + x4 = 16

The x term is 9x2.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x2 + 20.25 + x4 = 16 + 20.25

Reorder the terms:
20.25 + 9x2 + x4 = 16 + 20.25

Combine like terms: 16 + 20.25 = 36.25
20.25 + 9x2 + x4 = 36.25

Factor a perfect square on the left side:
(x2 + 4.5)(x2 + 4.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x2 + 4.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

x2 + 4.5 = 6.020797289 Simplifying x2 + 4.5 = 6.020797289 Reorder the terms: 4.5 + x2 = 6.020797289 Solving 4.5 + x2 = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = 6.020797289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 6.020797289 + -4.5 x2 = 6.020797289 + -4.5 Combine like terms: 6.020797289 + -4.5 = 1.520797289 x2 = 1.520797289 Simplifying x2 = 1.520797289 Take the square root of each side: x = {-1.233206102, 1.233206102}

Subproblem 2

x2 + 4.5 = -6.020797289 Simplifying x2 + 4.5 = -6.020797289 Reorder the terms: 4.5 + x2 = -6.020797289 Solving 4.5 + x2 = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = -6.020797289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -6.020797289 + -4.5 x2 = -6.020797289 + -4.5 Combine like terms: -6.020797289 + -4.5 = -10.520797289 x2 = -10.520797289 Simplifying x2 = -10.520797289 Reorder the terms: 10.520797289 + x2 = -10.520797289 + 10.520797289 Combine like terms: -10.520797289 + 10.520797289 = 0.000000000 10.520797289 + 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+4x+5)(3x^2-81)=0 | | x-1/2x=30 | | 5b+5b-25=5 | | 7x+3y=1800 | | Sin(7x)+sin(3x)=0 | | x-1/5x=12 | | -2x+5=-1+(-1)4x+7 | | 5b+2b-89=3 | | 4(u-3)-6= | | -2p-3(6-4p)=6(p-4)-14 | | 0.52+x=9.39 | | 5(x-1.2)=19 | | 2x-1+x=38 | | w=a/5 | | 26-(17-2x)=5x | | 550-315= | | -2/9(r)=-6 | | 4x^3-3000=0 | | 4x+7-6=5-4x+4 | | -2+y+x=0 | | 550=315+45+65 | | -27=72+9x | | -2/9(r)=6 | | k/3-7=25 | | 1+v=-15+5v | | 67=8a-7a+2 | | x/5=8/x | | x-0.92=4.69 | | 3a-5+4=6a | | y=6x+-7 | | -14x^2+32x-64=0 | | -10=5r+5 |

Equations solver categories