SOLUTION: Solve. try facoting first, it factoring is not possible or is difficult, use the quadratic formula. 2t^2-3t=1

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Question 834167: Solve. try facoting first, it factoring is not possible or is difficult, use the quadratic formula.
2t^2-3t=1
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
2t%5E2-3t=1
2t%5E2-3t-1=0

FACTORING:
We multiply the 2 that is in front of t%5E2 times the -1 at the end and get
2%2A%28-1%29=red%28-2%29 .
Now, we look for pairs of factors of red%28-2%29 that will ad up to the -3 in front of t.
We cannot find any pair that works.
We find 2%2A%28-1%29=red%28-2%29 and 1%2A%28-2%29=red%28-2%29 but the sums are wrong:
2%2B%28-1%29=1 and 1%2B%28-2%29=-1 .
If the coefficient in front of t was 1 or -1 ,
we could solve 2t%5E2%2Bt-1=0 or 2t%5E2-t-1=0 by factoring, but
we cannot solve 2t%5E2-3t-1=0 <--> 2t%5E2-3t=1 by factoring.

APPLYING THE QUADRATIC FORMULA:
The quadratic formula says that the solutions to ax%5E2%2Bbx%2Bc=0 are given by
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ .
In 2t%5E2-3t-1=0 we have t instead of x ,
but the name of the variable does not matter.
a=2 is the coefficient of the term with the variable squared.
b=-3 is the coefficient of the term with the variable not squared.
c=-1 is the independent term.
Applying the formula with those values substituted (and t instead of x , of course) we get
t+=+%28-%28-3%29+%2B-+sqrt%28%28-3%29%5E2-4%2A2%2A%28-1%29%29%29%2F%282%2A2%29+
t+=+%283+%2B-+sqrt%289%2B8%29%29%2F4+
highlight%28t+=+%283+%2B-+sqrt%2817%29%29%2F4%29
That is an ugly expression that says that the solutions are the irrational numbers
%283+%2B+sqrt%2817%29%29%2F4=approximately1.78
and
%283+-+sqrt%2817%29%29%2F4=approximately-0.28 .
No wonder factoring did not work.
Factoring can only work when the solutions are rational numbers.