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)