Find the values of m for -3 + sqrt(m+59) = m.

First, we'll impose the condition of existence of the
square root.

m  +59
>=0

m >= -59

The
interval of admissible values of m are [-59 ;
+infinite)

Now, we'll solve the
equation:

-3 + sqrt(m+59) =
m

sqrt(m+59) = m + 3

We'll
raise to square both sides:

m + 59 =
(m+3)^2

m + 59 = m^2 + 6m +
9

We'll move all terms to the right side and we'll use the
symmetric property:

 m^2 + 6m + 9 - m - 59 =
0

We'll combine like
terms:

m^2 + 5m - 50 = 0

We'll
apply the quadratic formula:

m1 = [-5+sqrt(25 +
200)]/2

m1 =
(-5+15)/2

m1 =
5

m2 =
(-5-15)/2

m2 =
-10

Since both values are in the interval of
admissible values, they are accepted.