To isolate \( w \) on one side of the equation \((w + 6)^2 = 40\), follow these steps:

1. **Apply the square root to both sides** of the equation:
   \[
   \sqrt{(w + 6)^2} = \pm \sqrt{40}
   \]

2. **Simplify**:
   \[
   w + 6 = \pm \sqrt{40}
   \]

3. **Simplify the square root**:
   \[
   \sqrt{40} = 2\sqrt{10}
   \]
   So, the equation becomes:
   \[
   w + 6 = \pm 2\sqrt{10}
   \]

4. **Subtract 6 from both sides** to isolate \( w \):
   \[
   w = -6 \pm 2\sqrt{10}
   \]

Now \( w \) is isolated, and the solution is:
\[
w = -6 + 2\sqrt{10} \quad \text{or} \quad w = -6 - 2\sqrt{10}
\]

Would you like more details or have any questions? Here are some related problems:

1. Isolate \( x \) in the equation \( (x - 3)^2 = 49 \).
2. Solve and isolate \( y \) in \( (y + 5)^2 = 64 \).
3. Find \( z \) by isolating it in \( (z + 2)^2 = 16 \).
4. Isolate \( k \) in the equation \( (k - 4)^2 = 81 \).
5. Solve for \( m \) in \( (m + 8)^2 = 100 \).

**Tip:** Always remember to simplify square roots where possible before isolating the variable.

Learn how to isolate w in the equation (w + 6)^2 = 40 with a step-by-step solution. This problem involves algebraic manipulation and solving quadratic equations, specifically using square root properties. Suitable for advanced high school students.

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