SOLUTION: Please help me solve this problem: Find k to make the trinomial a perfect square: r square + 10r + k Thank you, Carrie

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this problem: Find k to make the trinomial a perfect square: r square + 10r + k Thank you, Carrie      Log On


   

Question 236845: Please help me solve this problem:
Find k to make the trinomial a perfect square:
r square + 10r + k
Thank you, Carrie
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, perfect squares are of the form %28a%2Bb%29%5E2

In this case, we want a perfect square of the form %28r%2Bx%29%5E2 where 'x' is an unknown expression or number.


%28r%2Bx%29%5E2=r%5E2%2B10r%2Bk Set that perfect square expression equal to the given expression.


r%5E2%2B2rx%2Bx%5E2=r%5E2%2B10r%2Bk FOIL the left side.


2rx%2Bx%5E2=10r%2Bk Subtract r%5E2 from both sides.


Since the only terms with 'r' in them are 2rx and 10r, this means that 2rx=10r. Divide both sides by 'r' to get 2x=10. Now solve for 'x' to get x=5

So the left side of %28r%2Bx%29%5E2 becomes %28r%2B5%29%5E2. FOIL this expression out to get %28r%2B5%29%5E2=r%5E2%2B10r%2B25. So we see that the value of k is k=25.


Hopefully you understand this whole process (if not, just ask). Once you do, there is a handy shortcut. The value of 'k' is simply equal to half the coefficient of 'r' squared. In other words,

k=%2810%2F2%29%5E2=5%5E2=25 which is what we just got.