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

Apr 1, 2018

$n = 15 , - 8$

#### Explanation:

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

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

${n}^{2} - 7 n - 120 = 0$

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

$- 15 \cdot 8 = - 120$

Now, we have the following:

$\left(n - 15\right) \left(n + 8\right) = 0$

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

$n = 15$ & $n = - 8$

Hope this helps!

Apr 1, 2018

-8 and 15.

#### Explanation:

${n}^{2} - 7 n - 120 = 0$.
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.