if the square of a positive integer is added to 4 times te integer, the result is 437. Find the integer.

Question

if the square of a positive integer is added to 4 times te integer, the result is 437. Find the integer.

Answer 1

The square of a positive integer added to 4 times the integer is 437..

 

x² + 4x = 437

 

I chose to do this by completing the square..

 

x²+4x+4 = 437 + 4

(x+2)² = 441

Take square root of both sides

 

x+2 = ±√441

x = -2 ± 21

 

x = -23 or x = 19

 

We are told the variable is a positive integer, thus  x = 19

 

Check:  19² + 4(19) = 437

           361 + 76 = 437

               437 = 437

This answer checks

Answer 2

x² + 4x = 437

 

x²  + 4x -437 = 0

 

x = -b/2a + (b² -4ac)^1/2/2a is quadratic formula for positive root.

 

  = -4/2 + (4^{2 -} - 4(-437))^1/2

 

  = -2 + (16 + 1748)^1/2

 

  = -2 + (1764)^1/2

 

  = -2 + 42

 

= 40