Question

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

Answer 1

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

Answer 2

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.