Question

N^2-n/3=7 complete the square

Answer 1

Answer:

You need to add 1/36th to both sides of the equation, giving you the expression

$n^2 - \frac{1}{3}n + \frac{1}{36} = 7\frac{1}{36}$

Which can be expressed as:

$(n - \frac{1}{6})^2 = 7\frac{1}{36}$

Step-by-step explanation:

We need to add a term that is the the square of half the coefficient of the second term.

$n^2 - n/3 = 7\\n^2 - \frac{1}{3}n = 7\\n^2 - \frac{1}{3}n + \frac{1}{36} = 7\frac{1}{36}\\(n - \frac{1}{6})^2 = 7\frac{1}{36}$

Let's check the answer by expanding:

$(n - \frac{1}{6})^2 = 7\frac{1}{36}\\n^2 - \frac{1}{6}n - \frac{1}{6}n + \frac{1}{36} = 7\frac{1}{36}\\n^2 - \frac{1}{3}n + \frac{1}{36} = 7\frac{1}{36}\\n^2 - \frac{1}{3}n = 7$

Which verifies the answer.