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Question 572911: When 36 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.
Found 2 solutions by rfer, mathsmiles:
Answer by rfer(16322)   (Show Source):
Answer by mathsmiles(68)  (Show Source):
You can put this solution on YOUR website! 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!
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