Explain why the equation (x-4) ^2-10=15 has two solutions.

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.

Add 10 both sides

(x-4) ^2=25

sqrt both sides

remember to take positive and negative roots

x-4=+/-5

add 4

x=4+/-5

it is because the square of z is the same as the square of - z for example

it is becasue of of the property of squareing numbers