(k-7)2=16

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

(k-7)2⋅12=±16

Remove the perfect root factor k-7 under the radical to solve for k.

k-7=±16

Rewrite 16 as 42.

k-7=±42

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

k-7=±4

k-7=±4

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

k-7=4

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

Add 7 to both sides of the equation.

k=4+7

Add 4 and 7.

k=11

k=11

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

k-7=-4

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

Add 7 to both sides of the equation.

k=-4+7

Add -4 and 7.

k=3

k=3

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

k=11,3

k=11,3

Solve Using the Square Root Property (k-7)^2=16