a^4-12a^2+16=

Simple and best practice solution for a^4-12a^2+16= 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 a^4-12a^2+16= equation: 


Simplifying
a4 + -12a2 + 16 = 0

Reorder the terms:
16 + -12a2 + a4 = 0

Solving
16 + -12a2 + a4 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -12a2 + -16 + a4 = 0 + -16

Reorder the terms:
16 + -16 + -12a2 + a4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -12a2 + a4 = 0 + -16
-12a2 + a4 = 0 + -16

Combine like terms: 0 + -16 = -16
-12a2 + a4 = -16

The a term is -12a2.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12a2 + 36 + a4 = -16 + 36

Reorder the terms:
36 + -12a2 + a4 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + -12a2 + a4 = 20

Factor a perfect square on the left side:
(a2 + -6)(a2 + -6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(a2 + -6) equal to 4.472135955 and -4.472135955.


Subproblem 1
a2 + -6 = 4.472135955

Simplifying
a2 + -6 = 4.472135955

Reorder the terms:
-6 + a2 = 4.472135955

Solving
-6 + a2 = 4.472135955

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a2 = 4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + a2 = 4.472135955 + 6
a2 = 4.472135955 + 6

Combine like terms: 4.472135955 + 6 = 10.472135955
a2 = 10.472135955

Simplifying
a2 = 10.472135955

Take the square root of each side:
a = {-3.236067978, 3.236067978}


Subproblem 2
a2 + -6 = -4.472135955

Simplifying
a2 + -6 = -4.472135955

Reorder the terms:
-6 + a2 = -4.472135955

Solving
-6 + a2 = -4.472135955

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a2 = -4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + a2 = -4.472135955 + 6
a2 = -4.472135955 + 6

Combine like terms: -4.472135955 + 6 = 1.527864045
a2 = 1.527864045

Simplifying
a2 = 1.527864045

Take the square root of each side:
a = {-1.236067978, 1.236067978}


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-3.236067978, 3.236067978, -1.236067978, 1.236067978}

See similar equations:

| 80*0.35= | | 2(33)/11 | | 2*33/11 | | 12c^2+38c+20=0 | | 5x+2=5x+4 | | 2x/11=6 | | sec^2x+2secx=3 | | 5nsqare-67n+216=0 | | x-6(5+x)=15 | | 4x-7y+7=0 | | 3x+4=11+4(x-1) | | 3x+2y=150000 | | -3x^3(3x^5+8)= | | -5xy^3(8xy^2+6xy-7x)= | | 43+-7x=90 | | 2(6+1)+5(3+2)= | | 43-7x=90 | | -xy^5(9xy^2+9xy-8x)= | | x-0.01=372.13 | | 3/4x-1/4= | | 9x^3(8x^2-4x+2)= | | -6x(x-5)= | | -5y(4y+8)= | | 3[n-1]+6= | | 3x^5y^7+6x^6y^6=0 | | 9t^7(t-t^2+2t^3)= | | 5x(4x^2+x)= | | 7x-42.6=x | | 30t^2-25t=5t | | 2[n+4]-6= | | -4t+1=3+1-7t | | -2q+60=2q |

Equations solver categories