Respuesta :

apologiabiology
I"m guessing you mean
[tex] \sqrt{x+9} -5=x+4[/tex]
add 5 to both sides
[tex] \sqrt{x+9}=x+9[/tex]
square both sides
x+9=x²+18x+81
minus x+9 both sides
0=x²+17x+72
factor
what 2 numbres multiply to get 72 and add to get 17?
8 and 9
0=(x+8)(x+9)
set to zer

0=x+8
x=-8

x+9=0
x=-9

test each

[tex] \sqrt{-8+9} -5=-8+4[/tex]
[tex] \sqrt{1} -5=-4[/tex]
1-5=-4
-4=-4
true

[tex] \sqrt{-9+9} -5=-9+4[/tex]
[tex] \sqrt{0} -5=-5[/tex]
-5=-5
true


the solutions are x=-9 and -8
boffeemadrid

Answer:

x=8 and x=9

Step-by-step explanation:

The given equation is:

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

On solving this equation, we get

⇒[tex]\sqrt{x+9}=x+9[/tex]

Squaring on both sides, we get

⇒[tex]x+9=x^2+81+18x[/tex]

⇒[tex]x^2+18x-x-9+81=0[/tex]

⇒[tex]x^2+17x+72=0[/tex]

⇒[tex]x^2+8x+9x+72=0[/tex]

⇒[tex](x+8)(x+9)=0[/tex]

Thus, the solution of the above equations are x= 8 and x=9.

Otras preguntas