Can you solve the following using the square root property? [((x-3)^2) = 7]

To solve the equation \((x - 3)^2 = 7\) 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 \(a = \pm \sqrt{b}\).

So, take the square root of both sides of the equation:
\[
x - 3 = \pm \sqrt{7}
\]

### Step 2: Solve for \(x\)
Now, solve for \(x\) by isolating it on one side of the equation:
\[
x = 3 \pm \sqrt{7}
\]

### Step 3: Express the Final Solution
There are two possible solutions for \(x\):
\[
x = 3 + \sqrt{7} \quad \text{or} \quad x = 3 - \sqrt{7}
\]

These are the two solutions to the equation \((x - 3)^2 = 7\).

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

Here are 5 related questions:
1. How would you solve \((x + 5)^2 = 9\) using the square root property?
2. Can you explain how the square root property is different from factoring?
3. How would you solve a quadratic equation like \(x^2 - 4 = 0\)?
4. What happens if the number under the square root is negative?
5. How do you solve equations with multiple square roots?

**Tip:** Always remember to consider both the positive and negative square roots when applying the square root property!

Learn how to solve the quadratic equation (x-3)^2 = 7 using the square root property with a step-by-step breakdown. Understand key algebraic concepts and apply the square root formula to find both positive and negative solutions. Perfect for students in Grades 9-10.

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