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

(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
Simplify the right side of the equation.
Rewrite 36 as 62.
5k+4=±62
Pull terms out from under the radical, assuming positive real numbers.
5k+4=±6
5k+4=±6
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.
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