PreCalc
posted by Sheila on .
Could someone please check theseI had tried one last night but it was really wrong so I'm been workinghopefully these are correct.
What are the roots of the equation and answers have to be simplified
2x^2 + 5x10 =0
2x^2 + 5x10+10=0+10
2x^2 + 5x = 10
2x^2 + 5x/2 = 10/2
2x^2/2 + 5x/2 = 5
x^2 + 5/2x = 5
(5/2 * 1/2)^2 = 5/4^2
x^2 + 5/2x + (5/4)^2 = 5 + (5/4)^2
(x+5/4)^2 = 105/16
x + 5/4 = +minus sqrt 105/16 = sqrt 3^1 * 5^1*7^1 = sqrt 105/4
x= 5/4 + sqrt105/4 or x= 5/4  sqrt 105/4 Is this correct and simplified as far as it can be?
thank you Someone suggested a site that will do it but I want to learn on my own

at this point...
x^2 + 5/2x =5
you want to complete the square, take 1/2 of 5/2, square it, and add it to both sides.
x^2+5/2 x + 25/16=5+25/16=105/16
(x+5/4)^2=(sqrt 105/16)^2
so we agree. I didn't follow your work.
http://www.youtube.com/watch?v=xGOQYTo9AKY 
I thought that once I got to 105/16 I should take the square root which is factored out so I can't take anything out of the 105,however I can take the square root of 16 = 4 and you take the square root of (x+5/4)^2 to get it out of parentheses, so therefore the 2 roots are x= 5/4 + or minus square root of 105/4 as the simplified version