Subtracting a number from half its square gives a result of 13. Express the possible values of the number in the simplest radical form.

Question

This is a hard quadratic word problem. How do you come up with two equations? 

Answer 1

.5x² - x = 13

 

multiply by 2:

 

x² - 2x = 26

 

x² - 2x - 26 = 0

 

2 ± √((-2)² - 4*1*-26)

            2(1)

 

2 ± √108

     2

 

2± 6√3

     2

 

1 ± 3√3

Answer 2

x - 1/2 x² = 13

 

2x - x² = 26

 

-x² + 2x -26 = 0   solve this quadratic equation

 

x = ( -2 + √(4 - 104))/ -1= 2 + 10i

 

:)