Question

Carter is solving for x by the process of completing the square for the following

problem:

3x^2+ 12x-24 = 0

He got to this point below:

Type the number that goes in the "?" spot:

(x+?)2 = 12

Answer 1

The number that goes in place of the question mark is 2.

Explanation:

Let's solve it!

3x² + 12x - 24 = 0

First we can factor 3 out of each term:

x² + 4x - 8 = 0

Now we'll add 12 to both sides to complete the square:

x² + 4x + 4 = 12

And finish it off:

(x + 2)² = 12

So the answer to the question is 2

Bonus:

We can also now solve this for x:

(x + 2)² = 12

x = √12 - 2

x = 2√3 - 2

x ≈ 2 × ±1.732 - 2

x ≈ 1.464, -5.464