Use the square root property to solve the equation.

​(xminus−77​)squared2equals=81

To solve the equation \((x - 7)^2 = 81\) using the square root property, follow these steps:

### Step 1: Apply the square root property
The square root property states that if \(a^2 = b\), then \(a = \pm\sqrt{b}\).

Apply this property to the equation:
\[
(x - 7)^2 = 81
\]
\[
x - 7 = \pm\sqrt{81}
\]

### Step 2: Simplify the square root
Calculate the square root of 81:
\[
x - 7 = \pm 9
\]

### Step 3: Solve for \(x\)
Now, solve for \(x\) by adding 7 to both sides for each case:

**Case 1:** \(x - 7 = 9\)
\[
x = 9 + 7
\]
\[
x = 16
\]

**Case 2:** \(x - 7 = -9\)
\[
x = -9 + 7
\]
\[
x = -2
\]

### Final Answer
The solutions to the equation \((x - 7)^2 = 81\) are:
\[
x = 16 \quad \text{or} \quad x = -2
\]

Would you like further details on any step, or do you have any questions?

Here are five related questions for further exploration:
1. How would the solution change if the equation were \((x + 7)^2 = 81\)?
2. Can you solve the equation \((2x - 3)^2 = 49\) using the square root property?
3. What happens if the right-hand side of the equation is a negative number?
4. How can the square root property be applied to equations with complex solutions?
5. Can you solve the equation \(x^2 - 4x + 4 = 25\) using the square root property?

**Tip:** When using the square root property, always consider both the positive and negative square roots to ensure you find all possible solutions.

Learn how to solve the equation (x - 7)^2 = 81 using the square root property with detailed steps. Understand the application of square roots and find both possible solutions. Suitable for high school students and above.

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