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

Apr 1, 2018

$x = - 4$ & $x = - 8$

#### 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:

${x}^{2} + 12 x + 32 = 0$

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

$4 \cdot 8 = 32$

Thus, we have:

$\left(x + 4\right) \left(x + 8\right) = 0$

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

$x = - 4$ and $x = - 8$

Hope this helps!

Apr 1, 2018

-4, and - 8

#### Explanation:

$y = {x}^{2} + 12 x + 32 = 0$.
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.