x^4+32x^2-180=0

Simple and best practice solution for x^4+32x^2-180=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+32x^2-180=0 equation:


Simplifying
x4 + 32x2 + -180 = 0

Reorder the terms:
-180 + 32x2 + x4 = 0

Solving
-180 + 32x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 32x2 + 180 + x4 = 0 + 180

Reorder the terms:
-180 + 180 + 32x2 + x4 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 32x2 + x4 = 0 + 180
32x2 + x4 = 0 + 180

Combine like terms: 0 + 180 = 180
32x2 + x4 = 180

The x term is 32x2.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x2 + 256 + x4 = 180 + 256

Reorder the terms:
256 + 32x2 + x4 = 180 + 256

Combine like terms: 180 + 256 = 436
256 + 32x2 + x4 = 436

Factor a perfect square on the left side:
(x2 + 16)(x2 + 16) = 436

Calculate the square root of the right side: 20.880613018

Break this problem into two subproblems by setting 
(x2 + 16) equal to 20.880613018 and -20.880613018.

Subproblem 1

x2 + 16 = 20.880613018 Simplifying x2 + 16 = 20.880613018 Reorder the terms: 16 + x2 = 20.880613018 Solving 16 + x2 = 20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x2 = 20.880613018 + -16 Combine like terms: 16 + -16 = 0 0 + x2 = 20.880613018 + -16 x2 = 20.880613018 + -16 Combine like terms: 20.880613018 + -16 = 4.880613018 x2 = 4.880613018 Simplifying x2 = 4.880613018 Take the square root of each side: x = {-2.209210949, 2.209210949}

Subproblem 2

x2 + 16 = -20.880613018 Simplifying x2 + 16 = -20.880613018 Reorder the terms: 16 + x2 = -20.880613018 Solving 16 + x2 = -20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x2 = -20.880613018 + -16 Combine like terms: 16 + -16 = 0 0 + x2 = -20.880613018 + -16 x2 = -20.880613018 + -16 Combine like terms: -20.880613018 + -16 = -36.880613018 x2 = -36.880613018 Simplifying x2 = -36.880613018 Reorder the terms: 36.880613018 + x2 = -36.880613018 + 36.880613018 Combine like terms: -36.880613018 + 36.880613018 = 0.000000000 36.880613018 + 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:

| -4.8g=25.8 | | rt+u=4v | | 5x+(5x-20)=180 | | -(2x-1)-2(3x-1)=4(x+1)-2x | | (4x^3-7x^2+10x-4)-(3x^3-10x^2-8x+10)= | | 2(2k-1)=(k-2) | | -3+2x=x+1 | | -7x-6=12x-41 | | x^2(x+8)=20 | | 5(2x+9)=6(2x+13) | | -5x-9=-4x-14 | | 2+4(x-9)=-5(x+5) | | 11x-(8x-3)=27 | | x-y=y-10 | | 6x^2+24x-560= | | M(M+6)=-8 | | 2n^2+24n-600=0 | | 1.50(2)+1.50x=11.50 | | 49x^2-x-3=0 | | w-.2+2.5=.49(w-.75) | | 1.50(2x)+1.50=11.50 | | 2x+10=5x+7 | | 1.50(2)+1.50=11.50 | | 100x+50=150x+30 | | 7c-13-17c+23= | | 5y^2=8y-3 | | 52=16+6x | | 2x-9x+54=4x+32 | | 5(s-2)-10= | | 0.2(x+60)+.2x=16 | | 3a+6=2a-14 | | 18c-9+14c+36= |

Equations solver categories