The product of some negative number and 5 less than twice that number is 375. Find the number.

Question

The product of some negative number and 5 less than twice that number is 375. Find the number.

Answer 1

Here's what we know:

ab = 375 (the product of two numbers is 375)

b = 2a - 5 (five less than twice the other)

 

Plug in the variable value:

a(2a - 5) = 375

Distribute:

2a² - 5a = 375

subtract:

2a² - 5a - 375 = 0

 

Now to factor out. Let's look at possibilities:

√375 ≈ 19.36 (using that as a baseline because with the middle coefficient being only 5, the factorization is going to be fairly close)

15 * 25 = 375 (the last number of the parentheses needs to be the multiply to equal 375)

2 * -15 + 25 = -5 (the middle digits need to add/subtract together to equal -5. The 2 comes from the first coefficient value.)

(2a + 25)(a - 15) = 0

Since we know a needs to be negative, we can ignore the second set and focus on the first:

2a + 25 = 0

2a = -25

a = -12.5

 

b = 2 * -12.5 - 5

b = -25 - 5

b = -30

 

check:

-12.5 * -30 = 375

375 = 375

Answer 2

X is the negative number

 

2X - 5 is 5 less than twice the number

 

              X ( 2X - 5 ) = 375

 

                 2X² - 5X = 375

 

         2X² - 5X - 375 = 0

 

Factoring:

 

(2X + 25 ) (X - 15 )  = 0

 

2X + 25 = 0    ;  X - 15 = 0

 

     2X = -25   ;         X = 15 (has to be a negative number

 

      X = -12.5  is the number