What properties are used to solve (x-7)^2-4=0

To solve the equation \((x - 7)^2 - 4 = 0\), we can apply a combination of algebraic properties and steps. Here’s a breakdown of the key properties used:

### 1. **Isolate the squared term**: 
   - The first step is to isolate the squared term \((x - 7)^2\) on one side of the equation.
   - \((x - 7)^2 - 4 = 0\) becomes \((x - 7)^2 = 4\).

### 2. **Use the square root property**:
   - The next step is to apply the **square root property**, which states that if \(a^2 = b\), then \(a = \pm \sqrt{b}\).
   - So, taking the square root of both sides gives:
     \[
     x - 7 = \pm \sqrt{4}
     \]
     \[
     x - 7 = \pm 2
     \]

### 3. **Solve for \(x\)**:
   - Now, solve the resulting linear equations:
     \[
     x - 7 = 2 \quad \text{or} \quad x - 7 = -2
     \]
     \[
     x = 9 \quad \text{or} \quad x = 5
     \]

### 4. **Verify the solutions**:
   - Finally, substitute the values \(x = 9\) and \(x = 5\) back into the original equation to verify that they satisfy \((x - 7)^2 - 4 = 0\).

### The solution is: \(x = 5\) and \(x = 9\).

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Would you like more details on any of these steps? 

Here are 5 related questions to explore:
1. How is the square root property used to solve quadratic equations?
2. What are some other methods to solve quadratic equations, like factoring or completing the square?
3. Can all quadratic equations be solved using the square root method?
4. How can we verify solutions when solving quadratic equations?
5. What is the difference between solving quadratic equations by factoring and using the quadratic formula?

**Tip:** Always verify your solutions by substituting them back into the original equation!

What properties are used to solve (x-7)^2-4=0?

Learn how to solve the equation (x - 7)^2 - 4 = 0 with step-by-step guidance. This solution involves isolating the squared term, applying the square root property, and solving the resulting linear equations. Ideal for students in Grades 9-10 studying algebra and quadratic equations.

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