Explain why the equation (x-4)^2-10=15 has two solutions. then solve the equation to find the solutions. show all your work! (30 points)

Hello there,
Let's solve it first so that we can understand whats going on in the equation

(x-4)²-10=15
add 10 to both sides
(x-4)²=25
square root both sides

(Okay, so here is where the problem can have 2 solutions. Because the square root of 25 could be (5*5) or it could be (-5*-5). If it's positive five then...

x-4=5
add 4 to both sides
x=9

if it's negative 5 then...

x-4=-5
add 4 to both sides
x=-1

So the answer could be x=-1 or x=9.

It has two solutions because there are two possibilities for the answer to the square root of 25.

I hope this help, and if you have any more questions, please feel free to ask me.
Have a nice day!