Let's solve the given equation [tex]\(2x^2 - 4x = 14\)[/tex] by completing the square.
1. Start with the given equation:
[tex]\[
2x^2 - 4x = 14
\][/tex]
2. Move the constant term to the left side to set the equation to zero:
[tex]\[
2x^2 - 4x - 14 = 0
\][/tex]
3. Factor out the coefficient of [tex]\( x^2 \)[/tex] from the terms that involve [tex]\( x \)[/tex]:
[tex]\[
2(x^2 - 2x) = 14
\][/tex]
4. To complete the square, we need to add and subtract the same value inside the parenthesis. The term to complete the square is found by taking half the coefficient of [tex]\( x \)[/tex] (which is [tex]\(-2\)[/tex]), and squaring it:
[tex]\[
\left(\frac{-2}{2}\right)^2 = 1
\][/tex]
5. Add and subtract this square term inside the parenthesis:
[tex]\[
2(x^2 - 2x + 1 - 1) = 14
\][/tex]
6. This simplifies to:
[tex]\[
2((x - 1)^2 - 1) = 14
\][/tex]
7. Distribute the 2 across the terms inside the parenthesis:
[tex]\[
2(x - 1)^2 - 2 = 14
\][/tex]
8. Move the constant term [tex]\(-2\)[/tex] to the right side:
[tex]\[
2(x - 1)^2 - 2 + 2 = 14 + 2
\][/tex]
9. Simplify the equation:
[tex]\[
2(x - 1)^2 = 16
\][/tex]
10. Divide by 2 to isolate the square term:
[tex]\[
(x - 1)^2 = 8
\][/tex]
Thus, the equation simplifies to the form:
[tex]\[
(x - 1)^2 = 8
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{B}
\][/tex]
