Question
Solve the equation
Solve for n
Solve for v
n=−∣v∣v,v=0n=∣v∣v,v=0
Evaluate
v=v2n2
Swap the sides of the equation
v2n2=v
Divide both sides
v2v2n2=v2v
Divide the numbers
n2=v2v
Divide the numbers
More Steps

Evaluate
v2v
Use the product rule aman=an−m to simplify the expression
v2−11
Subtract the terms
v11
Simplify
v1
n2=v1
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±v1
Simplify the expression
More Steps

Evaluate
v1
To take a root of a fraction,take the root of the numerator and denominator separately
v1
Simplify the radical expression
v1
Multiply by the Conjugate
v×v1×v
Calculate
∣v∣1×v
Calculate
∣v∣v
n=±∣v∣v
Separate the equation into 2 possible cases
n=∣v∣vn=−∣v∣v
Calculate
{n=−∣v∣vv=0{n=∣v∣vv=0
Solution
n=−∣v∣v,v=0n=∣v∣v,v=0
Show Solution
