how to interpret word problems into quadratic formula

Question

The square of a positive integer minus twice its consecutive integer is equal to 22. find the integers. by using the quadratic formula 

Answer 1

Let N be the positive integer.

 

"The square of a positive integer" is N²

 

"minus twice its consecutive integer" is -2(N + 1)

 

"is equal to 22" is 22

 

Put it all together and get:

 

N² - 2(N + 1) = 22

N² - 2N - 2 - 22 = 0

 

N² - 2N - 24 = 0

 

This is the quadratic equation that you seek.

 

Note that

 

N² - 2N - 24 = (N + 4)(N - 6)

 

There are two solutions for N:  N = -4, 6.  Since N is positive, then N = 6 is the solution, and N + 1 = 7 is its consecutive integer.

Answer 2

Let the integer = x

Let the consecutive integer = x + 1

 

 

"Square" means to raise the number to the power of 2. "Minus" means to subtract.

 

x² - (x + 1)² = 22

 

 

Now just expand the equation and simplify.