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

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
Simplify each side of the equation.
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
Solve for l.
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
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

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