Question

Question #70e44

Answer 1

`x in {+5, +2}`

Explanation:

Case `1`: the absolute value is positive

`3m = m^2 - 10`

`0 = m^2 - 3m - 10`

`0 = (m - 5)(m + 2)`

`m = 5 or -2`

Case `2`: the absolute value is negative

`3m = -(m^2 - 10)`

`3m = -m^2 +10`

`m^2 + 3m - 10 = 0`

`(m + 5)(m - 2) = 0`

`m = -5 or 2`

However, the negative solutions are extraneous because the left hand side would be negative while the right hand side would be positive (by the definition of `|a|`).

Hopefully this helps!