# Solve for v v^4-13v^2+36=0 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
Factor u2-13u+36 using the AC method.
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 and solve.
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 and solve.
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
Solve the equation for v.
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
Solve the equation for v.
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

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