Question

How do you solve `x^2-10x+25=0` algebraically?

Answer 1

`x = 5`

Explanation:

Start off by writing the brackets `(x + )(x +)`, because you know this will feature in the answer, given that there's an `x^2`.

Now you want to find two numbers that add together to make `-10` and multiply together to make `25`. Use trial and error by writing down or thinking about the factors of `25`, and then which ones add to `-10`. You should come to `-5` and `-5`.

This gives the brackets `(x-5)(x-5)` or `(x-5)^2 = 0`

Now change around the equation to make `x` the subject.

`(x-5)^2 = 0`
`x-5 = sqrt0`
`x-5 = 0`
`x = 5`