# Thread: quadratic equation, why does using one way not yield the same results as another

1. ## quadratic equation, why does using one way not yield the same results as another

I need to solve for t in the problem

-t^2 + 2t = 1/2

If I complete the square I get the correct answer 1-[sqrt2/2] or 1+[sqrt2/2]

if I use the quadratic formula [-b +/- (b^2 -4ac)/2a) I don't get the same answer. or I am doing something wrong.

Why is this? And how do I know which one to use so that I don't get the wrong answer. Thank you!

2. ## Re: quadratic equation, why does using one way not yield the same results as another

Show us your calculation how your got different answes we'll be able to tell you what did you do wrong.

Also you would need to write (sqrt(2)/2) not sqrt2/2

3. ## Re: quadratic equation, why does using one way not yield the same results as another

okay.

-t^2 + 2t = 1/2 I write it in standard form making it -t^2 + 2t - (1/2) = 0

and then I put it into the quadratic formula. -2 +/- Sqrt[2^2 - (4*-1*-1/2)]/2(-1) --> -2 +/- sqrt(2)/2 and thats as far as I get with that one

for completing the square.

[-t^2 + 2t = 1/2] times its by -1 --> [t^2 - 2t = -1/2. then I take the coefficient of t being 2, I times it by 1/2 and square it then add it to both sides. I get

[t^2 - 2t + 1 = 1/2] then I factor getting (t-1)^2 = 1/2 then I eliminate the exponent --> t-1 = 1/sqrt(2) and finish off solving for t getting t= 1+ 1/sqrt(2)
or t = 1 - 1/sqrt(2)