How can I solve the equation x² + 8x + 3 = 0 using the completing the square method?

To solve the quadratic equation x² + 8x + 3 = 0 using the completing the square method, follow these steps:

Start with the original equation:
```
x² + 8x + 3 = 0
```
Isolate the constant:
```
x² + 8x = -3
```
Complete the square:
To complete the square, we need to add and subtract the square of half the coefficient of x. The coefficient of x is 8, so:

Half of 8 is 4, and squaring it gives us:
```
(4)² = 16
```
Add 16 to both sides of the equation:
```
x² + 8x + 16 = -3 + 16
```
Simplify:
```
x² + 8x + 16 = 13
```
Factor the left side:
Now the left side can be factored into a perfect square:
```
(x + 4)² = 13
```
Take the square root of both sides:
Taking the square root gives us:
```
x + 4 = ±√13
```
Isolate x:
Finally, we isolate x:
```
x = -4 ± √13
```

This results in two potential solutions:

And that’s how you solve the equation x² + 8x + 3 = 0 using the completing the square method!