To solve the equation $(x + 7)^2 - 11 = 0$ for $x$, follow these steps:

Step 1: Isolate the squared term

Add 11 to both sides of the equation:

$(x + 7)^2 = 11$

Step 2: Take the square root of both sides

Take the square root of both sides of the equation:

$x + 7 = \pm \sqrt{11}$

Step 3: Solve for $x$

Now, solve for $x$ by subtracting 7 from both sides:

$x = -7 \pm \sqrt{11}$

Step 4: Calculate the numerical values

Since we need to round to two decimal places, calculate the value of $\sqrt{11}$:

$\sqrt{11} \approx 3.32$

So, the solutions are:

$x_1 = -7 + 3.32 \approx -3.68$ $x_2 = -7 - 3.32 \approx -10.32$

Step 5: Order the solutions

From least to greatest, the solutions are:

$\boxed{-10.32 \text{ and } -3.68}$

Would you like any further details or have any questions?

Here are five related questions for further practice:

1. Solve $(x + 5)^2 - 20 = 0$ and round to two decimal places.
2. Find the solutions to $(x - 8)^2 - 15 = 0$ and round to two decimal places.
3. Solve $(x + 3)^2 - 7 = 0$ for $x$ and round to two decimal places.
4. Determine the zeros of $(x - 6)^2 - 12 = 0$ and round to two decimal places.
5. Solve for $x$ in $(x + 4)^2 - 13 = 0$ and round to two decimal places.

Tip: When dealing with square roots, always consider both the positive and negative roots.