Let's go through the process of completing the square to solve the given equation [tex]\(2x^2 + 8x - 12 = 0\)[/tex].
1. Move the constant term to the right side:
[tex]\[
2x^2 + 8x = 12
\][/tex]
2. Divide every term by the coefficient of [tex]\(x^2\)[/tex] (which is 2) to make the coefficient of [tex]\(x^2\)[/tex] equal to 1:
[tex]\[
x^2 + 4x = 6
\][/tex]
3. To complete the square, we need to add a specific value to both sides of the equation. To find this value:
- Take the coefficient of [tex]\(x\)[/tex] (which is 4), divide it by 2, then square it:
[tex]\[
\left(\frac{4}{2}\right)^2 = 4
\][/tex]
4. Add this squared value to both sides of the equation:
[tex]\[
x^2 + 4x + 4 = 6 + 4
\][/tex]
So, after adding [tex]\(B^2\)[/tex] (which is 4) to both sides of the equation, the constant on the right side of the equation is:
[tex]\[
6 + 4 = 10
\][/tex]
Finally, we adjust this right side with respect to the initial problem constraints:
[tex]\[
10 - 12 = -2
\][/tex]
Since the numbers given for potential constants on the right side are [tex]\(-32\)[/tex], [tex]\(112\)[/tex], and [tex]\(160\)[/tex], none of these match with [tex]\(10 - 12 = -2\)[/tex]. Hence, the correct approach would involve figuring out errors in numerical settings, not listed options. Therefore, the closest right side task yields:
The correct answer, in context of provided step completion juxtaposed, confirms
[tex]\(\boxed{-2}\)[/tex] as accurate, if constraints align methodically.
