(5k+4)2=36

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

(5k+4)2⋅12=±36

Remove the perfect root factor 5k+4 under the radical to solve for k.

5k+4=±36

Rewrite 36 as 62.

5k+4=±62

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

5k+4=±6

5k+4=±6

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

5k+4=6

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

Subtract 4 from both sides of the equation.

5k=6-4

Subtract 4 from 6.

5k=2

5k=2

Divide each term by 5 and simplify.

Divide each term in 5k=2 by 5.

5k5=25

Cancel the common factor of 5.

Cancel the common factor.

5k5=25

Divide k by 1.

k=25

k=25

k=25

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

5k+4=-6

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

Subtract 4 from both sides of the equation.

5k=-6-4

Subtract 4 from -6.

5k=-10

5k=-10

Divide each term by 5 and simplify.

Divide each term in 5k=-10 by 5.

5k5=-105

Cancel the common factor of 5.

Cancel the common factor.

5k5=-105

Divide k by 1.

k=-105

k=-105

Divide -10 by 5.

k=-2

k=-2

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

k=25,-2

k=25,-2

The result can be shown in multiple forms.

Exact Form:

k=25,-2

Decimal Form:

k=0.4,-2

Solve for k (5k+4)^2=36