# Pre-Calc

Could someone please check these-I had tried one last night but it was really wrong so I'm been working-hopefully these are correct.

What are the roots of the equation and answers have to be simplified
2x^2 + 5x-10 =0
2x^2 + 5x-10+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

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1. 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

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bobpursley
2. 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

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