how to solve this quadratic word problem

Question

the product of a positive number and four more than the number is 32. what is the number?

Answer 1

The wording of the problem translates into algebra as

 

x(x + 4) = 32

 

x² + 4x - 32 = 0

 

This factors into

 

(x - 4)(x + 8) = 0

 

Solutions are x = 4 and -8.  Since you want a positive solution, keep only x = 4.

Answer 2

Choose the first let statement to mean x. The second let statement represents (x + 4).  The two let statements are the factors of the product x(x + 4). This is x^2 + 4x = 32. Subtract 32 from both members of the equation to set it in standard form equal to zero. Then solve with the quadratic formula giving {-4 (+/-) [4^2 - 4(1)(-32)]^1/2}/[2(1)]. Simplifying produces -2 (+/-) 6 = (4,-8).

Choose 4, the only positive root.