Question

How do you solve `sqrt(3m+28) =m`?

Answer 1

`color(blue)( m=7`

Explanation:

`sqrt(3m+28) =m`

Squaring both sides
`(sqrt(3m+28))^2 =m^2`

`3m +28=m^2`

`m^2 - 3m -28=0`

Factorising by splitting the middle term (in order to find the solutions)**

`m^2 - color(green)(3m) -28=0`

`m^2 - color(green)(7m +4m) -28=0`

`m(m-7) +4 (m-7)=0`

`(m+4)(m-7) =0`

Upon equating the factors with zero we can obtain solutions:

`m+4=0, m=-4`
This solution is not applicable as square root of an expression cannot be negative

So the solution is
`(m-7) =0, m=7`