Find the value of x so the distance between the points A(3,5) and B(x,8) is 5 units.

The problem provides the length of the segment `AB = 5` , hence,
using Pythagorean theorem yields:

`AB^2 = (3 - x)^2 + (5 - 8)^2 `

`5^2 = 9 - 6x + x^2 + 9 => 25 - 18 = x^2 -
6x`

`x^2 - 6x - 7 = 0`

You may use the
factorization to evaluate the solutions to quadratic equation, such
that:

`x^2 - 7x + x - 7 = 0 => (x^2 - 7x) + (x - 7) =
0`

`x(x - 7) + (x - 7) = 0 => (x - 7)(x + 1) = 0 =>
{(x - 7 = 0),(x + 1 = 0):} => {(x = 7),(x = -1):}
`

Hence, evaluating the missing coordinate x yields
that there exists two points whose y coordinate is `y = 8` , such that:` x = 7, B(7,8)` and
`x = -1, B (-1,8).`