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
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
To solve the quadratic equation 2x^2 + 5x - 10 = 0, you can use the quadratic formula. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients of the equation.
In this case, a = 2, b = 5, and c = -10. Substituting these values into the quadratic formula, we get:
x = (-5 ± √(5^2 - 4 * 2 * -10)) / (2 * 2).
Simplifying further, we have:
x = (-5 ± √(25 + 80)) / 4,
x = (-5 ± √105) / 4.
So the roots of the equation are:
x = (-5 + √105) / 4 and x = (-5 - √105) / 4.
These roots cannot be simplified any further, so your answers, x = (-5 + √105) / 4 and x = (-5 - √105) / 4, are correct and simplified as much as possible.