Question 572911
Let X = a number we're looking for.


If we subtract 36 from the square of that number, X^2 - 36 ... 
The result is equal to 5 times the number, 5X
Therefore, 
X^2 - 36 = 5X


You've probably seen this solved by putting the equation in the form:
aX^2 - bX - c = 0


Doing that here, we subtract 5X from both sides to make the right side of the equation equal to zero.

X^2 - 5X - 36 = 0
Now we need to factor this.

(X _  _   )(X _  _  ) = 0 (where _ denotes an operator or term that we need.)
Looking at the operators, we see that the operands are different, so
(X - _  )(X +  _  ) = 0   (we have operator, need term.)
Now we need to find two factors of 36 whose difference is 5.  So let's try a few:
36 = 6 X 6  Nope
36 = 12 X 3 Nope
36 = 9 X 4  Yup!


Since the middle term is negative, we know the placement of the 9 and 4.
(X-9)(X+4)= 0
Therefore, X-9=0   or X+4=0
X-9=0  => X=9
X+4=0  => X=-4


Going back to the original problem, it says "Find the negative solution." 
Therefore, X=-4.


Let's check:
(-4)^2-36 = 5*(-4)
16-36 = -20
-20=-20  Check!