Question

Find a negative real number such that the square of the sum of the number and 25 is equal to 36

Answer 1

"The square of the sum of the number and 25 is equal to 36" translates to 
$(n+25)^2=36$

Take square root of both sides:

$|n+25|=6\quad\Longrightarrow\quad n+25 = 6\ \text{ or }\ n+25=-6$

Then subtract both sides by 25:

$n = 6-25\ \text{ or }\ n=-6-25\\\ \\\boxed{n=-19\ \text{or}\ n=-31}$

Hope this helps.