SOLUTION: Solve for T: {t-1}^2 = {2t^2-8t+6} ***I know that this can only have at most 2 answers because the degree of the polynomial is 2. I know that {t-1}^2 is {t-1}{t-1} and that

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve for T: {t-1}^2 = {2t^2-8t+6} ***I know that this can only have at most 2 answers because the degree of the polynomial is 2. I know that {t-1}^2 is {t-1}{t-1} and that      Log On


   

Question 213950: Solve for T:
{t-1}^2 = {2t^2-8t+6}

***I know that this can only have at most 2 answers because the degree of the polynomial is 2. I know that {t-1}^2 is {t-1}{t-1} and that 2t^2-8t+6 is simplified to 2{t^2-4t+3}. I have tried to simplify it more but keep getting stuck and I know that one of the answers for t=1, but I cant find the other! Any help would be appreciated!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28t-1%29%5E2+=+2t%5E2-8t%2B6 Start with the given equation.


t%5E2-2t%2B1+=+2t%5E2-8t%2B6 FOIL


t%5E2-2t%2B1-2t%5E2%2B8t-6=0 Get every term to the left side.


-t%5E2%2B6t-5=0 Combine like terms.


Notice that the quadratic -t%5E2%2B6t-5 is in the form of At%5E2%2BBt%2BC where A=-1, B=6, and C=-5


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%28-1%29%28-5%29+%29%29%2F%282%28-1%29%29 Plug in A=-1, B=6, and C=-5


t+=+%28-6+%2B-+sqrt%28+36-4%28-1%29%28-5%29+%29%29%2F%282%28-1%29%29 Square 6 to get 36.


t+=+%28-6+%2B-+sqrt%28+36-20+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-5%29 to get 20


t+=+%28-6+%2B-+sqrt%28+16+%29%29%2F%282%28-1%29%29 Subtract 20 from 36 to get 16


t+=+%28-6+%2B-+sqrt%28+16+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


t+=+%28-6+%2B-+4%29%2F%28-2%29 Take the square root of 16 to get 4.


t+=+%28-6+%2B+4%29%2F%28-2%29 or t+=+%28-6+-+4%29%2F%28-2%29 Break up the expression.


t+=+%28-2%29%2F%28-2%29 or t+=++%28-10%29%2F%28-2%29 Combine like terms.


t+=+1 or t+=+5 Reduce.


So the solutions are t+=+1 or t+=+5