3+3b+1=b

Subtract 3 from both sides of the equation.

3b+1=b-3

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

3b+12=(b-3)2

Multiply the exponents in ((3b+1)12)2.

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

(3b+1)12⋅2=(b-3)2

Cancel the common factor of 2.

Cancel the common factor.

(3b+1)12⋅2=(b-3)2

Rewrite the expression.

(3b+1)1=(b-3)2

(3b+1)1=(b-3)2

(3b+1)1=(b-3)2

Simplify.

3b+1=(b-3)2

3b+1=(b-3)2

Simplify (b-3)2.

Rewrite (b-3)2 as (b-3)(b-3).

3b+1=(b-3)(b-3)

Expand (b-3)(b-3) using the FOIL Method.

Apply the distributive property.

3b+1=b(b-3)-3(b-3)

Apply the distributive property.

3b+1=b⋅b+b⋅-3-3(b-3)

Apply the distributive property.

3b+1=b⋅b+b⋅-3-3b-3⋅-3

3b+1=b⋅b+b⋅-3-3b-3⋅-3

Simplify and combine like terms.

Simplify each term.

Multiply b by b.

3b+1=b2+b⋅-3-3b-3⋅-3

Move -3 to the left of b.

3b+1=b2-3⋅b-3b-3⋅-3

Multiply -3 by -3.

3b+1=b2-3b-3b+9

3b+1=b2-3b-3b+9

Subtract 3b from -3b.

3b+1=b2-6b+9

3b+1=b2-6b+9

3b+1=b2-6b+9

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

b2-6b+9=3b+1

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

Subtract 3b from both sides of the equation.

b2-6b+9-3b=1

Subtract 3b from -6b.

b2-9b+9=1

b2-9b+9=1

Move 1 to the left side of the equation by subtracting it from both sides.

b2-9b+9-1=0

Subtract 1 from 9.

b2-9b+8=0

Factor b2-9b+8 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 8 and whose sum is -9.

-8,-1

Write the factored form using these integers.

(b-8)(b-1)=0

(b-8)(b-1)=0

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

b-8=0

b-1=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

b-8=0

Add 8 to both sides of the equation.

b=8

b=8

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

b-1=0

Add 1 to both sides of the equation.

b=1

b=1

The final solution is all the values that make (b-8)(b-1)=0 true.

b=8,1

b=8,1

Exclude the solutions that do not make 3+3b+1=b true.

b=8

Solve for b 3+ square root of 3b+1=b