Question

How do you solve `(2s-1)^{2}=225`?

Answer 1

`x=-7` or `x=8`

Explanation:

There is a rule that states `(a+b)^2=a^2+2ab+b^2`

In this case, `a` is `2s` and `b` is `-1`.

Therefore

`4s^2-4s+1=225`

Subtract `225` from both sides.

`4s^2-4s-224=0`

Divide by `4`.

`s^2-s-56=0`

You can factorise this as follows :

`(x+7)(x-8)`

Set each factor equal to `0`.

`x+7=0`
`x=-7`

`x-8=0`
`x=8`

Answer 2

`s = 8 or s = -7`

Explanation:

Although this equation leads to a quadratic trinomial, it is in the form `x^2 =c" "` so we can just find the square root of both sides,

`(2s-1)^2 = 225`

`2s-1 = +-sqrt225`

`2s = +-sqrt225+1`

`s = (+15+1)/2 = 8`

`s = (-15+1)/2 = -7`