SOLUTION: Solve. Check for extraneous solutions. Question: Square root of quantity (3x+7)= x - 1 I keep getting x= 2 or -3, but when I check it they numbers dont work out. Please show

Algebra ->  Radicals -> SOLUTION: Solve. Check for extraneous solutions. Question: Square root of quantity (3x+7)= x - 1 I keep getting x= 2 or -3, but when I check it they numbers dont work out. Please show      Log On


   

Question 546144: Solve. Check for extraneous solutions.
Question: Square root of quantity (3x+7)= x - 1
I keep getting x= 2 or -3, but when I check it they numbers dont work out. Please show all the steps.
Thanks!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Square root of quantity sqrt%283x%2B7%29 = x - 1
Square both sides
3x + 7 = (x-1)^2
FOIL the right side
3x + 7 = x^2 - 2x + 1
Combine like terms on the right
0 = x^2 - 2x - 3x + 1 - 7
A quadratic equation
x^2 - 5x - 6 = 0
Factors to
(x-6)(x+1) = 0
Two solutions
x = 6
x = -1
Check both solutions in the original equation
x=6
sqrt%283%286%29%2B7%29 = 6 - 1
sqrt%2825%29 = 6 - 1
5 = 5; x=6 is a good solution
x=-1
sqrt%283%28-1%29%2B7%29 = -1 - 1
sqrt%284%29 = -2
2 = -2, an extraneous solution