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

Math
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.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
Simplify the right side of the equation.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
Simplify the right side of the equation.
Tap for more steps…
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.
Tap for more steps…
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

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

Solve all your Math Problems: https://elanyachtselection.com/

We can solve all your math problems
Scroll to top