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

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) (Show Source): You can put this solution on YOUR website!
Remember, perfect squares are of the form

In this case, we want a perfect square of the form where 'x' is an unknown expression or number.

Set that perfect square expression equal to the given expression.

FOIL the left side.

Subtract from both sides.

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

So the left side of becomes . FOIL this expression out to get . 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,

which is what we just got.

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