9l+81=l+5

To remove the radical on the left side of the equation, square both sides of the equation.

9l+812=(l+5)2

Multiply the exponents in ((9l+81)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(9l+81)12⋅2=(l+5)2

Cancel the common factor of 2.

Cancel the common factor.

(9l+81)12⋅2=(l+5)2

Rewrite the expression.

(9l+81)1=(l+5)2

(9l+81)1=(l+5)2

(9l+81)1=(l+5)2

Simplify.

9l+81=(l+5)2

9l+81=(l+5)2

Simplify (l+5)2.

Rewrite (l+5)2 as (l+5)(l+5).

9l+81=(l+5)(l+5)

Expand (l+5)(l+5) using the FOIL Method.

Apply the distributive property.

9l+81=l(l+5)+5(l+5)

Apply the distributive property.

9l+81=l⋅l+l⋅5+5(l+5)

Apply the distributive property.

9l+81=l⋅l+l⋅5+5l+5⋅5

9l+81=l⋅l+l⋅5+5l+5⋅5

Simplify and combine like terms.

Simplify each term.

Multiply l by l.

9l+81=l2+l⋅5+5l+5⋅5

Move 5 to the left of l.

9l+81=l2+5⋅l+5l+5⋅5

Multiply 5 by 5.

9l+81=l2+5l+5l+25

9l+81=l2+5l+5l+25

Add 5l and 5l.

9l+81=l2+10l+25

9l+81=l2+10l+25

9l+81=l2+10l+25

Since l is on the right side of the equation, switch the sides so it is on the left side of the equation.

l2+10l+25=9l+81

Move all terms containing l to the left side of the equation.

Subtract 9l from both sides of the equation.

l2+10l+25-9l=81

Subtract 9l from 10l.

l2+l+25=81

l2+l+25=81

Move 81 to the left side of the equation by subtracting it from both sides.

l2+l+25-81=0

Subtract 81 from 25.

l2+l-56=0

Factor l2+l-56 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -56 and whose sum is 1.

-7,8

Write the factored form using these integers.

(l-7)(l+8)=0

(l-7)(l+8)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

l-7=0

l+8=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

l-7=0

Add 7 to both sides of the equation.

l=7

l=7

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

l+8=0

Subtract 8 from both sides of the equation.

l=-8

l=-8

The final solution is all the values that make (l-7)(l+8)=0 true.

l=7,-8

l=7,-8

Exclude the solutions that do not make 9l+81=l+5 true.

l=7

Solve for l square root of 9l+81=l+5