# Solve for a square root of 41-a=a+1 41-a=a+1
To remove the radical on the left side of the equation, square both sides of the equation.
41-a2=(a+1)2
Simplify each side of the equation.
Multiply the exponents in ((41-a)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(41-a)12⋅2=(a+1)2
Cancel the common factor of 2.
Cancel the common factor.
(41-a)12⋅2=(a+1)2
Rewrite the expression.
(41-a)1=(a+1)2
(41-a)1=(a+1)2
(41-a)1=(a+1)2
Simplify.
41-a=(a+1)2
41-a=(a+1)2
Solve for a.
Simplify (a+1)2.
Rewrite (a+1)2 as (a+1)(a+1).
41-a=(a+1)(a+1)
Expand (a+1)(a+1) using the FOIL Method.
Apply the distributive property.
41-a=a(a+1)+1(a+1)
Apply the distributive property.
41-a=a⋅a+a⋅1+1(a+1)
Apply the distributive property.
41-a=a⋅a+a⋅1+1a+1⋅1
41-a=a⋅a+a⋅1+1a+1⋅1
Simplify and combine like terms.
Simplify each term.
Multiply a by a.
41-a=a2+a⋅1+1a+1⋅1
Multiply a by 1.
41-a=a2+a+1a+1⋅1
Multiply a by 1.
41-a=a2+a+a+1⋅1
Multiply 1 by 1.
41-a=a2+a+a+1
41-a=a2+a+a+1
Add a and a.
41-a=a2+2a+1
41-a=a2+2a+1
41-a=a2+2a+1
Since a is on the right side of the equation, switch the sides so it is on the left side of the equation.
a2+2a+1=41-a
Move all terms containing a to the left side of the equation.
Add a to both sides of the equation.
a2+2a+1+a=41
Add 2a and a.
a2+3a+1=41
a2+3a+1=41
Move 41 to the left side of the equation by subtracting it from both sides.
a2+3a+1-41=0
Subtract 41 from 1.
a2+3a-40=0
Factor a2+3a-40 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 -40 and whose sum is 3.
-5,8
Write the factored form using these integers.
(a-5)(a+8)=0
(a-5)(a+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.
a-5=0
a+8=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
a-5=0
Add 5 to both sides of the equation.
a=5
a=5
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
a+8=0
Subtract 8 from both sides of the equation.
a=-8
a=-8
The final solution is all the values that make (a-5)(a+8)=0 true.
a=5,-8
a=5,-8
Exclude the solutions that do not make 41-a=a+1 true.
a=5
Solve for a square root of 41-a=a+1

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