Question

Find the non-extraneous solutions of the square root of the quantity (x plus 9) minus 5 equals quantity x plus 4.
x = −2
x = −9 and x = −2
x = 9
x = −9 and x = −8

Answer 1

\[\sqrt{x + 9}- 5 = x + 4\]

Answer 2

@eta

Answer 3

Add \(5\) to both the sides..

Answer 4

you want to isolate the root so that you can square both sides which you can then form a quadratic and solve for x

substitute your x values into the original equation and you will find that only one of them or both of them will work

Answer 5

And after that, square both the sides..

Answer 6

x = -9 ?

Answer 7

Oh, let me check, I have not solved it..

Answer 8

wait i got x^2 + 18x + 81

Answer 9

for the right hand side yes

Answer 10

\[x+9 = (x+9)^2\]

Answer 11

subtract the left hand side from the right hand side to make it equal to 0

Answer 12

then solve the quadratic

Answer 13

Do you have answer?

Answer 14

Have not you got this?