When the sum of 5 and twice a positive number is subtracted from the square of the number,0 results. Find the number.

Question

When the sum of 5 and twice a positive number is subtracted from the square of the number,0 results. Find the number.

Answer 1

x² - (5+2x) = 0   ;  x>0

 

We have a quadratic

 

x² - 2x - 5 = 0

 

Use the quadratic formula

x = [-b±√(b²-4ac)]/2a  ;  a=1, b=-2, c=-5

 

x = [2±√((-2)²-4(1)(-5))]/2

x = [2±√24]/2

x =(2±2√6)/2

x = 1 ± √6

 

Since we know x must be positive we can discard 1-√6

 

x = 1 + √6