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

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

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