SOLUTION: I can't quite figure this one out. The value for t=6 but I can't see how we get there. Greg t squared-t/2=15

Algebra ->  Equations -> SOLUTION: I can't quite figure this one out. The value for t=6 but I can't see how we get there. Greg t squared-t/2=15      Log On


   

Question 74153This question is from textbook
: I can't quite figure this one out. The value for t=6 but I can't see how we get there. Greg

t squared-t/2=15 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28t%5E2-t%29%2F2=15Start with the given equation
%281%2F2%29t%5E2-%281%2F2%29t=15Rewrite the equation
%281%2F2%29t%5E2-%281%2F2%29t-15=0Get all terms to one side. Now we can solve for t by using the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 0.5t%5E2%2B-0.5t%2B-15+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-0.5%29%5E2-4%2A0.5%2A-15=30.25.

Discriminant d=30.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--0.5%2B-sqrt%28+30.25+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-0.5%29%2Bsqrt%28+30.25+%29%29%2F2%5C0.5+=+6
t%5B2%5D+=+%28-%28-0.5%29-sqrt%28+30.25+%29%29%2F2%5C0.5+=+-5

Quadratic expression 0.5t%5E2%2B-0.5t%2B-15 can be factored:
0.5t%5E2%2B-0.5t%2B-15+=+0.5%28t-6%29%2A%28t--5%29
Again, the answer is: 6, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B-0.5%2Ax%2B-15+%29

So t=-5 and t=6