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
Accepted Solution
A:
Answer:Option d) x = 25Step-by-step explanation:we have[tex]\sqrt{x-9}+4=8[/tex]Solve for xSubtract 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 truethereforex=25 is a solution2) For x=-7[tex]\sqrt{-7-9}=4[/tex][tex]\sqrt{-16}=4[/tex]The radicand cannot be a negative numberthereforex=-7 is not a solution