v4-13v2+36=0

Substitute u=v2 into the equation. This will make the quadratic formula easy to use.

u2-13u+36=0

u=v2

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 36 and whose sum is -13.

-9,-4

Write the factored form using these integers.

(u-9)(u-4)=0

(u-9)(u-4)=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-9=0

u-4=0

Set the first factor equal to 0.

u-9=0

Add 9 to both sides of the equation.

u=9

u=9

Set the next factor equal to 0.

u-4=0

Add 4 to both sides of the equation.

u=4

u=4

The final solution is all the values that make (u-9)(u-4)=0 true.

u=9,4

Substitute the real value of u=v2 back into the solved equation.

v2=9

(v2)1=4

Solve the first equation for v.

v2=9

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

v=±9

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

Simplify the right side of the equation.

Rewrite 9 as 32.

v=±32

Pull terms out from under the radical, assuming positive real numbers.

v=±3

v=±3

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.

v=3

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

v=-3

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

v=3,-3

v=3,-3

v=3,-3

v=3,-3

Solve the second equation for v.

(v2)1=4

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

(v2)1⋅11=41

Remove the perfect root factor v2 under the radical to solve for v.

v2=41

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

v=±41

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

Simplify the right side of the equation.

Evaluate 41 as 4.

v=±4

Rewrite 4 as 22.

v=±22

Pull terms out from under the radical, assuming positive real numbers.

v=±2

v=±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.

v=2

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

v=-2

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

v=2,-2

v=2,-2

v=2,-2

v=2,-2

The solution to v4-13v2+36=0 is v=3,-3,2,-2.

v=3,-3,2,-2

Solve for v v^4-13v^2+36=0