Question

How do you solve `n^2-120=7n`?

Answer 1

`n=15,-8`

Explanation:

Whenever we're dealing with quadratics, we want to set them equal to zero, to find the zeroes.

We can start by subtracting `7n` from both sides to get:

`n^2-7n-120=0`

Now, we need to think of two numbers that sum up to `-7` and their product is `-120`. Since their product is negative, the signs are different.

After some trial and error, we arrive at `-15` and `8`, as

`-15+8=-7`

and

`-15*8=-120`

Now, we have the following:

`(n-15)(n+8)=0`

To find the zeroes, we just take the inverse signs to get:

`n=15` & `n=-8`

Hope this helps!

Answer 2

-8 and 15.

Explanation:

`n^2 - 7n - 120 = 0`.
Solve this equation by the new Transforming Method (Socratic, Google Search), case a = 1.
Find 2 real roost, that have opposite signs (ac < 0), knowing their sum (- b = 7) and their product (c = -120).
They are: - 8 and 15.

Note . This method avoids the lengthy factoring by grouping and solving the 2 binomials.