When 36 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.

n = -4

Step-by-step explanation:

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!

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)