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

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
Simplify each side of the equation.
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
Solve for b.
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

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