D=c+va⋅(forv)
Rewrite the equation as c+va⋅(forv)=D.
c+va⋅(forv)=D
Combine f and va.
c+fva(orv)=D
Combine o and fva.
c+o(fv)a(rv)=D
Combine r and o(fv)a.
c+r(o(fv))av=D
Combine r(o(fv))a and v.
c+r(o(fv))va=D
Raise v to the power of 1.
c+r(o(f(v1v)))a=D
Raise v to the power of 1.
c+r(o(f(v1v1)))a=D
Use the power rule aman=am+n to combine exponents.
c+r(o(fv1+1))a=D
Add 1 and 1.
c+r(o(fv2))a=D
c+rofv2a=D
Subtract c from both sides of the equation.
rofv2a=D-c
Multiply both sides of the equation by a.
rofv2=D⋅(a)-c⋅a
Multiply -c by a.
rofv2=Da-ca
Divide each term in rofv2=Da-ca by rof.
rofv2rof=Darof+-carof
Simplify rofv2rof.
Cancel the common factor of r.
Cancel the common factor.
rofv2rof=Darof+-carof
Rewrite the expression.
ofv2of=Darof+-carof
ofv2of=Darof+-carof
Cancel the common factor of o.
Cancel the common factor.
ofv2of=Darof+-carof
Rewrite the expression.
fv2f=Darof+-carof
fv2f=Darof+-carof
Cancel the common factor of f.
Cancel the common factor.
fv2f=Darof+-carof
Divide v2 by 1.
v2=Darof+-carof
v2=Darof+-carof
v2=Darof+-carof
Move the negative in front of the fraction.
v2=Darof-carof
v2=Darof-carof
Take the square root of both sides of the equation to eliminate the exponent on the left side.
v=±Darof-carof
Simplify the right side of the equation.
Combine the numerators over the common denominator.
v=±Da-carof
Factor a out of Da-ca.
Factor a out of Da.
v=±aD-carof
Factor a out of -ca.
v=±aD+a(-c)rof
Factor a out of aD+a(-c).
v=±a(D-c)rof
v=±a(D-c)rof
Rewrite a(D-c)rof as a(D-c)rof.
v=±a(D-c)rof
Multiply a(D-c)rof by rofrof.
v=±a(D-c)rof⋅rofrof
Combine and simplify the denominator.
Multiply a(D-c)rof and rofrof.
v=±a(D-c)rofrofrof
Raise rof to the power of 1.
v=±a(D-c)rofrofrof
Raise rof to the power of 1.
v=±a(D-c)rofrofrof
Use the power rule aman=am+n to combine exponents.
v=±a(D-c)rofrof1+1
Add 1 and 1.
v=±a(D-c)rofrof2
Rewrite rof2 as rof.
Use axn=axn to rewrite rof as (rof)12.
v=±a(D-c)rof((rof)12)2
Apply the power rule and multiply exponents, (am)n=amn.
v=±a(D-c)rof(rof)12⋅2
Combine 12 and 2.
v=±a(D-c)rof(rof)22
Cancel the common factor of 2.
Cancel the common factor.
v=±a(D-c)rof(rof)22
Divide 1 by 1.
v=±a(D-c)rofrof
v=±a(D-c)rofrof
Simplify.
v=±a(D-c)rofrof
v=±a(D-c)rofrof
v=±a(D-c)rofrof
Simplify the numerator.
Combine using the product rule for radicals.
v=±a(D-c)(rof)rof
Remove unnecessary parentheses.
v=±a(D-c)rofrof
v=±a(D-c)rofrof
Reorder factors in ±a(D-c)rofrof.
v=±arof(D-c)rof
v=±arof(D-c)rof
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=arof(D-c)rof
Next, use the negative value of the ± to find the second solution.
v=-arof(D-c)rof
The complete solution is the result of both the positive and negative portions of the solution.
v=arof(D-c)rof
v=-arof(D-c)rof
v=arof(D-c)rof
v=-arof(D-c)rof
v=arof(D-c)rof
v=-arof(D-c)rof
Solve for v D=c+v/a*(forv)