Need help please!!! thanks!!!

Question

The square of a negative number is 24 more than 2 times the negative number. Find the number.

 

The number = ____

Answer 1

(x)^2 = 24 + 2x

 

Subtract 2x to both sides

 

(x)^2 - 2x = 24

 

Subtract 24 to both sides

 

(x)^2 - 2x - 24 = 0

 

Factor

 

(x - 6) (x + 4) = 0

 

Set each expression equal to zero

 

x - 6 = 0

x = 6

 

x + 4 = 0

x = -4

 

 

The questions asks for a negative number, so the answer is -4

Answer 2

First we need to read through the problem and write an equation. The parentheses are what the words mean in numerical terms:

The square (^2) of a negative number (x) is (=) 24 more than (+24) 2 times the negative number (2x)

so:

x^2=24+2x

solve:

x^2-2x-24=0

(x+4)(x-6)=0

solving for both x:

x+4=0

x=-4

 

x-6=0

x=6

 

in this case since the problem specifies that the answer is a negative number, we know that x=-4

Plug it back in to check the answer:

x^2=24+2x

(-4)^2=24+2(-4)

16=24-8

16=16

so our answer is correct