(v-3)2-27=0

Add 27 to both sides of the equation.

(v-3)2=27

Take the square root of each side of the equation to set up the solution for v

(v-3)2⋅12=±27

Remove the perfect root factor v-3 under the radical to solve for v.

v-3=±27

Rewrite 27 as 32⋅3.

Factor 9 out of 27.

v-3=±9(3)

Rewrite 9 as 32.

v-3=±32⋅3

v-3=±32⋅3

Pull terms out from under the radical.

v-3=±33

v-3=±33

First, use the positive value of the ± to find the first solution.

v-3=33

Add 3 to both sides of the equation.

v=33+3

Next, use the negative value of the ± to find the second solution.

v-3=-33

Add 3 to both sides of the equation.

v=-33+3

The complete solution is the result of both the positive and negative portions of the solution.

v=33+3,-33+3

v=33+3,-33+3

The result can be shown in multiple forms.

Exact Form:

v=33+3,-33+3

Decimal Form:

v=8.19615242…,-2.19615242…

Solve for v (v-3)^2-27=0