if two times a number is subtracted from three the result is twenty-one less than the square number

Question

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Answer 1

Translate the words into equations:

 

two times a number:  2x

is subtracted from three: 3 -

the result is: =

 twenty-one less than the square of the number: x² - 21

 

Putting this together:  3 - 2x = x² - 21

 

add 2x to both sides

3 = x² + 2x - 21

subtract 3 from both sides

x² + 2x - 24 = 0

 

Now we have a quadratic.  Can it be factored?

What are the factors of -24 that add to 2?  6(-4) = -24;  6 - 4 = 2

 

x² + 2x - 24 = 0

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

This will be zero if either x+6=0  or  x-4=0

x = -6 or x = 4