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

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) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Square both sides

FOIL

Get everything to the right side

Combine like terms.

Factor

or Set each factor equal to zero

or Solve

So the possible solutions are or

However, if you plug in , you'll find that it is NOT a solution

So the only solution is
Answer by RAY100(1637) (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)
RELATED QUESTIONS
Help! I am stuck on solving a radical equation. The original problem is this:... (answered by tutorcecilia)
to solve sqrt x + sqrt x-5=5 for x, begin with which of these steps? a. isolate on... (answered by Alan3354)
To solve √(x+√x-5=5 for x, begin with which step? A. Combine the two... (answered by Alan3354)
True or false: the equation is too complicated to use the "isolate the radical, then... (answered by Boreal)
please help me answer this equation 1. Which of the following is/are true statement/s? (answered by MathLover1)
Find all real solutions of the quadratic equation. (Enter NONE if a solution does not... (answered by Alan3354,stanbon)
In order to solve a quadratic equation by completing the square, place the letter of the... (answered by edjones)
solve and check the quadratic equation below by taking the square root of both sides.... (answered by stanbon)
x^2+x+ the square root of (x^2+x) -2 =0. I know to iscolate the radical one one side of... (answered by Earlsdon)