a4-9a2+14=0

Substitute u=a2 into the equation. This will make the quadratic formula easy to use.

u2-9u+14=0

u=a2

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 14 and whose sum is -9.

-7,-2

Write the factored form using these integers.

(u-7)(u-2)=0

(u-7)(u-2)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

u-7=0

u-2=0

Set the first factor equal to 0.

u-7=0

Add 7 to both sides of the equation.

u=7

u=7

Set the next factor equal to 0.

u-2=0

Add 2 to both sides of the equation.

u=2

u=2

The final solution is all the values that make (u-7)(u-2)=0 true.

u=7,2

Substitute the real value of u=a2 back into the solved equation.

a2=7

(a2)1=2

Solve the first equation for a.

a2=7

Take the square root of both sides of the equation to eliminate the exponent on the left side.

a=±7

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

a=7

Next, use the negative value of the ± to find the second solution.

a=-7

The complete solution is the result of both the positive and negative portions of the solution.

a=7,-7

a=7,-7

a=7,-7

Solve the second equation for a.

(a2)1=2

Take the 1th root of each side of the equation to set up the solution for a

(a2)1⋅11=21

Remove the perfect root factor a2 under the radical to solve for a.

a2=21

Take the square root of both sides of the equation to eliminate the exponent on the left side.

a=±21

The complete solution is the result of both the positive and negative portions of the solution.

Evaluate 21 as 2.

a=±2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

a=2

Next, use the negative value of the ± to find the second solution.

a=-2

The complete solution is the result of both the positive and negative portions of the solution.

a=2,-2

a=2,-2

a=2,-2

a=2,-2

The solution to a4-9a2+14=0 is a=7,-7,2,-2.

a=7,-7,2,-2

The result can be shown in multiple forms.

Exact Form:

a=7,-7,2,-2

Decimal Form:

a=2.64575131…,-2.64575131…,1.41421356…,-1.41421356…

Solve for a a^4-9a^2+14=0