Question

Solve for all possible values of x.

square root of the quantity x minus 9 end quantity plus 4 equals 8

a) x = −5
b) x = 7
c) x = 13
d)x = 25

Answer 1

Option d) x = 25

Explanation:

we have

`√(x-9)+4=8`

Solve for x

Subtract 4 both sides

`√(x-9)+4-4=8-4`

`√(x-9)=4`

squared both sides

`(x-9)=(+/-)4^2`

`(x-9)=(+/-)16`

Adds 9 both sides

`x=9(+/-)16`

`x1=9(+)16=25`

`x2=9(-)16=-7`

Verify

1) For x=25

`√(25-9)=4`

`√(16)=4`

`4=4` ----> is true

therefore

x=25 is a solution

2) For x=-7

`√(-7-9)=4`

`√(-16)=4`

The radicand cannot be a negative number

therefore

x=-7 is not a solution