Question

How do you solve `(x-2)^2-25=0`?

Answer 1

`x=7`

`x=-3`

Explanation:

`(x-2)^2-25=0`

or

`(x-2)^2=25`

or

`x-2=sqrt25`

or

`x-2=+-5`

or

`x=2+-5`

or

`x=2+5`

or

`x=7`---------------------------------Ans `1`

or

`x=2-5`

or

`x=-3`-----------------------------Ans `2`

Answer 2

`x=7,x=-3`

Explanation:

First step is to isolate the `(x-2)^2` term

add 25 to both sides.

`rArr(x-2)^2-cancel(25)+cancel(25)=0+25`

`rArr(x-2)^2=25`

now take the `color(blue)"square root of both sides"`

`sqrt((x-2)^2)=+-sqrt25`

`rArrx-2=+-5`

solve : `x-2=5rArrx=5+2=7`

solve : `x-2=-5rArrx=-5+2=-3`

Answer 3

`x=7` or `x=-3`

Explanation:

We can use identity `(a^2-b^2)=(a-b)(a+b)`. As such

`(x-2)^2-25=0`

`hArr(x-2)^2-5^2=0`

or `(x-2-5)(x-2+5)=0`

or `(x-7)(x+3)=0`

i.e. `x=7` or `x=-3`