State the value of k that makes each expression a perfect square trinomial. Then, write the trinomial as the square of a binomial: p^2 - 5p + k. (I have some steps that I don't understand.)

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State the value of k that makes each expression a perfect square trinomial. Then, write the trinomial as the square of a binomial: p^2 - 5p + k. (I have some steps that I don't understand.)

Mathematics
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coefficient of p = -5 coefficient of p / 2 = -5/2 (coefficient of p / 2)^2 = (-5/2)^2 = 25/4
p^2 - 5p + 25/4 = -k + 25/4 (p-5/2)^2 = +- 25/4 p = -5/2 +- 5/2
the answer has to be 6.25

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To find k 1) Take the coefficient of p = -5 2) Divide this answer by 2 = -5/2 3) Square this answer = 25/4 So we have p^2 - 5p + 25/4. Now factor this expression (p - 5/2)(p - 5/2) or (p - 5/2)^2
ohhh..
\[\frac{1}{2}\times5=\frac{5}{2}, (\frac{5}{2})^2=\frac{25}{4}=6.25\]
so add 6.25 to complete the square.

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