**Solve for \[x\]. Enter the solutions from least to greatest.**
*Round to two decimal places.*

\[(x + 7)^2 - 11 = 0\]

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.

Learn how to solve the quadratic equation (x + 7)^2 - 11 = 0 step-by-step with detailed explanations and rounding to two decimal places. Understand the application of the quadratic formula and square roots in solving algebraic equations.

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