To rewrite the given quadratic equation [tex]\( x^2 + 4x + 1 = 10 \)[/tex] by completing the square, follow these steps:
1. Move the constant term to the other side:
[tex]\[
x^2 + 4x + 1 - 10 = 0
\][/tex]
Simplify it to:
[tex]\[
x^2 + 4x - 9 = 0
\][/tex]
2. Shift the constant term on the left side to the right:
[tex]\[
x^2 + 4x = 9
\][/tex]
3. To complete the square, find the constant needed to form a perfect square trinomial.
Start by taking half of the coefficient of [tex]\( x \)[/tex] (which is 4), then squaring it:
[tex]\[
\left(\frac{4}{2}\right)^2 = 4
\][/tex]
4. Add and subtract this constant (4) inside the equation:
[tex]\[
x^2 + 4x + 4 - 4 = 9
\][/tex]
Combine the terms to get:
[tex]\[
x^2 + 4x + 4 = 9 + 4
\][/tex]
5. Rewrite the left-hand side as a square:
[tex]\[
(x + 2)^2 = 13
\][/tex]
Thus, the equivalent form of the quadratic equation [tex]\( x^2 + 4x + 1 = 10 \)[/tex] after completing the square is:
[tex]\[
(x + 2)^2 = 13
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{B. (x + 2)^2 = 13}
\][/tex]
