B. $$ x^{2}+2 x-65=0 \Rightarrow x^{2}+2 x=65 \Rightarrow x^{2}+2 x+\square=65 $$

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UpStudy AI · Accepted Answer

To complete the square for the equation:

$$
x^{2} + 2x - 65 = 0
$$

Follow these steps:

1. **Move the constant term to the other side:**

$$
   x^{2} + 2x = 65
   $$

2. **Determine the term to complete the square:**

The coefficient of $$ x $$ is 2. To complete the square, take half of this coefficient and square it:

$$
   \left(\frac{2}{2}\right)^2 = 1
   $$

So, you need to add **1** to both sides of the equation.

3. **Add the term to both sides:**

$$
   x^{2} + 2x + 1 = 65 + 1
   $$
   
   Simplifying:

$$
   (x + 1)^2 = 66
   $$

4. **Solve for $$ x $$:**

$$
   x + 1 = \pm \sqrt{66}
   $$
   
   $$
   x = -1 \pm \sqrt{66}
   $$

**Final Answer:**  
You should add **1** to complete the square.
To complete the square, add **1** to both sides of the equation $$ x^{2} + 2x = 65 $$.

B.

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