To solve the equation [tex]\(x^2 + 4x = 14\)[/tex] by completing the square, follow these steps:
1. Start with the given equation:
[tex]\[
x^2 + 4x = 14
\][/tex]
2. Identify the coefficient of [tex]\(x\)[/tex]:
The coefficient of [tex]\(x\)[/tex] is 4.
3. Calculate [tex]\((b/2)^2\)[/tex], where [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex]:
[tex]\[
b = 4
\][/tex]
[tex]\[
\left(\frac{b}{2}\right)^2 = \left(\frac{4}{2}\right)^2 = 2^2 = 4
\][/tex]
4. Add and subtract this value [tex]\((4)\)[/tex] to the left side of the equation:
[tex]\[
x^2 + 4x + 4 - 4 = 14
\][/tex]
5. Rewrite the equation so that the left-hand side forms a perfect square:
Combining terms properly:
[tex]\[
(x + 2)^2 - 4 = 14
\][/tex]
6. Move the constant term [tex]\(-4\)[/tex] to the right-hand side of the equation:
[tex]\[
(x + 2)^2 = 14 + 4
\][/tex]
[tex]\[
(x + 2)^2 = 18
\][/tex]
Therefore, the correctly completed square form of the equation [tex]\(x^2 + 4x = 14\)[/tex] is:
[tex]\[
(x + 2)^2 = 18
\][/tex]
Thus, the correct choice is:
[tex]\[
\boxed{D. (x+2)^2 = 18}
\][/tex]
