# Solve for v D=c+v/a*(forv) D=c+va⋅(forv)
Rewrite the equation as c+va⋅(forv)=D.
c+va⋅(forv)=D
Multiply va(forv).
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
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 by rof and simplify.
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
The complete solution is the result of both the positive and negative portions of the solution.
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.
Factor a out of -ca.
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
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)

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