(5y-3)2=9

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

(5y-3)2⋅12=±9

Remove the perfect root factor 5y-3 under the radical to solve for y.

5y-3=±9

Rewrite 9 as 32.

5y-3=±32

Pull terms out from under the radical, assuming positive real numbers.

5y-3=±3

5y-3=±3

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

5y-3=3

Move all terms not containing y to the right side of the equation.

Add 3 to both sides of the equation.

5y=3+3

Add 3 and 3.

5y=6

5y=6

Divide each term by 5 and simplify.

Divide each term in 5y=6 by 5.

5y5=65

Cancel the common factor of 5.

Cancel the common factor.

5y5=65

Divide y by 1.

y=65

y=65

y=65

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

5y-3=-3

Move all terms not containing y to the right side of the equation.

Add 3 to both sides of the equation.

5y=-3+3

Add -3 and 3.

5y=0

5y=0

Divide each term by 5 and simplify.

Divide each term in 5y=0 by 5.

5y5=05

Cancel the common factor of 5.

Cancel the common factor.

5y5=05

Divide y by 1.

y=05

y=05

Divide 0 by 5.

y=0

y=0

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

y=65,0

y=65,0

The result can be shown in multiple forms.

Exact Form:

y=65,0

Decimal Form:

y=1.2,0

Mixed Number Form:

y=115,0

Solve for y (5y-3)^2=9