SOLUTION: square root of 2x+11=x+4 Isolate a radical on one side, square both sides, solve the resulting equation

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Question 191751: square root of 2x+11=x+4 Isolate a radical on one side, square both sides, solve the resulting equation
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B11%29=x%2B4 Start with the given equation.


2x%2B11=%28x%2B4%29%5E2 Square both sides


2x%2B11=x%5E2%2B8x%2B16 FOIL


0=x%5E2%2B8x%2B16-2x-11 Get everything to the right side


0=x%5E2%2B6x%2B5 Combine like terms.


0=%28x%2B5%29%28x%2B1%29 Factor


x%2B5=0 or x%2B1=0 Set each factor equal to zero


x=-5 or x=-1 Solve


So the possible solutions are x=-5 or x=-1


However, if you plug in x=-5, you'll find that it is NOT a solution


So the only solution is x=-1

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
sq rt (2x+11) = (x+4)
square both sides
(2x+11) = (x+4)^2 = x^2 +8x +16
0= x^2 +6x +5
0 = ( x+5) (x+1)
x= -5, and x=-1 however
since we squared we MUST check both answers
checking x= (-1)
( 2(-1) +11 ) ^1/2 = ( (-1) + 4 )
(9)^1/2 =3 =3 ok therefore x= (-1) is valid
checking x= (-5)
( 2(-5) +11 )^1/2 = (-5) +4
(1)^ 1/2 = -1
1 = -1 questionable
while (1)^1/2 does equal (+1) and (-1)
commonly we must question validity of x= (-5)