Question

How do you solve `5x^2 - 125 = 0`?

Answer 1

Start by factorizing.

Explanation:

Start by factorizing

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

then you can divide both sides by 5 and since `0/5 =0` you get the expression:

`x^2 - 25 = 0`

rearrange so that 25 is on the right hand side

`x^2 =25`

`x=± sqrt25`

`x=± 5`

Answer 2

`x = +- 5`

Explanation:

To make progress, an attempt should be made to have just `x` on one side of the equation to see what it is equal to (on the other side of the equation).

By inspection, both `5` and `-125` are divisible by `5`. Zero is also divisible by `5` in the sense `0/5 = 0`

So, dividing both sides of the equation by `5` (also called "dividing through by `5`)

`5x^2 - 125 = 0`

implies

`(5x^2)/5 - (125)/5 = 0/5`

that is

`x^2 - 25 = 0`

Now `25` may be added to both sides to give

`x^2 - 25 + 25 = 0 + 25`

that is

`x^2 = 25`

You will recognise `25` as a perfect square so finding a solution should be easy but take care! Remember square numbers have two roots, a positive one and a negative one. So

`x^2 = 25`

implies

`sqrt(x^2) = sqrt(25)`

that is

`x = 5`
or
`x = -5`