SOLUTION: Please help me solve: {{{(t-5)^2=2(5-t)}}} Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve: {{{(t-5)^2=2(5-t)}}} Thank you.      Log On


   

Question 206666This question is from textbook Introductory Algebra
: Please help me solve:
%28t-5%29%5E2=2%285-t%29
Thank you. This question is from textbook Introductory Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28t-5%29%5E2=2%285-t%29 Start with the given equation.


t%5E2-10t%2B25=2%285-t%29 FOIL


t%5E2-10t%2B25=10-2t Distribute


t%5E2-10t%2B25-10%2B2t=0 Get all terms to the left side.


t%5E2-8t%2B15=0 Combine like terms.


Notice that the quadratic t%5E2-8t%2B15 is in the form of At%5E2%2BBt%2BC where A=1, B=-8, and C=15


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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2815%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-8, and C=15


t+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2815%29+%29%29%2F%282%281%29%29 Negate -8 to get 8.


t+=+%288+%2B-+sqrt%28+64-4%281%29%2815%29+%29%29%2F%282%281%29%29 Square -8 to get 64.


t+=+%288+%2B-+sqrt%28+64-60+%29%29%2F%282%281%29%29 Multiply 4%281%29%2815%29 to get 60


t+=+%288+%2B-+sqrt%28+4+%29%29%2F%282%281%29%29 Subtract 60 from 64 to get 4


t+=+%288+%2B-+sqrt%28+4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


t+=+%288+%2B-+2%29%2F%282%29 Take the square root of 4 to get 2.


t+=+%288+%2B+2%29%2F%282%29 or t+=+%288+-+2%29%2F%282%29 Break up the expression.


t+=+%2810%29%2F%282%29 or t+=++%286%29%2F%282%29 Combine like terms.


t+=+5 or t+=+3 Simplify.


So the solutions are t+=+5 or t+=+3