Respuesta :

Answer:

(x - 3)^2 = 24.

Step-by-step explanation:

x^2 -6x - 15 = 0

(x - 3)^2 - 9 - 15 = 0

(x - 3^2 -24 = 0

(x - 3)^2 = 24.

Recalling that

[tex](x-a)^2=x^2-2ax+a^2[/tex]

Let's compare the middle term:

[tex]-6x = -2ax \iff a=3[/tex]

So, we want to complete

[tex](x-3)^2 = x^2-6x+9[/tex]

Which differs from [tex]x^2-6x-15[/tex] by 24. So, if we add 24 to both sides, we have

[tex]x^2-6x-15=0 \iff x^2-6x+9=24 \iff (x-3)^2=24[/tex]