Question

How do you solve `x^2+12x=-32`?

Answer 1

`x=-4` & `x=-8`

Explanation:

Whenever we're dealing with quadratics, we want to set them equal to zero. We can do this by adding `32` to both sides. Thus, we have:

`x^2+12x+32=0`

Next, we need to think of 2 numbers that sum to `12` and their product is `32`. Since both the sum and product is positive, the two numbers will both be positive.

After some trial and error, we arrive at `4` and `8`, as:

`4+8=12`

and

`4*8=32`

Thus, we have:

`(x+4)(x+8)=0`

The zeroes will be the opposite sign, and we get:

`x=-4` and `x=-8`

Hope this helps!

Answer 2

-4, and - 8

Explanation:

`y = x^2 + 12x + 32 = 0`.
Solve this equation by the new Transforming Method (Socratic, Google Search), Case a = 1.
Find 2 real roots, that are both negative (ac > 0; ab > 0) knowing their sum (- b = - 12) and their product (c = 32).
They are: -4 and - 8.

Note . This method directly gives the 2 real roots. We don't have to factor by grouping and to solve the 2 binomials.