Answer:
Option d) x = 25
Step-by-step explanation:
we have
[tex]\sqrt{x-9}+4=8[/tex]
Solve for x
Subtract 4 both sides
[tex]\sqrt{x-9}+4-4=8-4[/tex]
[tex]\sqrt{x-9}=4[/tex]
squared both sides
[tex](x-9)=(+/-)4^2[/tex]
[tex](x-9)=(+/-)16[/tex]
Adds 9 both sides
[tex]x=9(+/-)16[/tex]
[tex]x1=9(+)16=25[/tex]
[tex]x2=9(-)16=-7[/tex]
Verify
1) For x=25
[tex]\sqrt{25-9}=4[/tex]
[tex]\sqrt{16}=4[/tex]
[tex]4=4[/tex] ----> is true
therefore
x=25 is a solution
2) For x=-7
[tex]\sqrt{-7-9}=4[/tex]
[tex]\sqrt{-16}=4[/tex]
The radicand cannot be a negative number
therefore
x=-7 is not a solution
