+0  
 
-2
25
5
avatar+816 

Help plz!

 

The equation $18+5x^2=20x + 20$ has two distinct solutions. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?

 Aug 10, 2023
 #1
avatar+757 
+1

5x^2-20x-2=0. Using the quadratic formula, we get (20+-sqrt(440))/10. We can turn this into (20+-2sqrt(110))/10, or (10+-sqrt(110))/5. I calculated both answers, and got 4 and 0. 4*0 = 0, so I think the answer is 0. 

 Aug 10, 2023
 #2
avatar+757 
+1

Yooooo I finished quicker then CPhill. 

history  Aug 10, 2023
 #4
avatar+129376 
0

good job, history  !!!!!

 

 

cool cool cool

CPhill  Aug 10, 2023
 #3
avatar+129376 
+1

18 + 5x^2 = 20x + 20

 

Rearrange as

 

5x^2 - 20x - 2  =  0      divide through by 2

 

x^2 -10x - 1  =  0

 

x^2 -10x  =  1             complete the  square on  x

 

x^2 - 10x + 25 =  1 + 25

 

(x - 5)^2  =  26

 

x -5 =   sqrt (26)   and -sqrt (26)

 

x = sqrt (26) + 5      →  rounded =  10

 

x= -sqrt (26) + 5   →   rounded  =  0 

 

Product =   10 * 0  =  0

 

cool cool cool

 Aug 10, 2023

2 Online Users

avatar
avatar