Solve the quadratic equation using the square root property: 4(x−5)^2=28. 

To solve the equation \(4(x - 5)^2 = 28\) using the square root property, we can follow these steps:

### Step 1: Isolate \((x - 5)^2\)
\[
4(x - 5)^2 = 28
\]
Divide both sides by 4:
\[
(x - 5)^2 = \frac{28}{4} = 7
\]

### Step 2: Apply the Square Root Property
Now that we have \((x - 5)^2 = 7\), we can take the square root of both sides. Remember to consider both the positive and negative roots:
\[
x - 5 = \pm \sqrt{7}
\]

### Step 3: Solve for \(x\)
Add 5 to both sides to isolate \(x\):
\[
x = 5 \pm \sqrt{7}
\]

### Final Answer
The solutions to the equation are:
\[
x = 5 + \sqrt{7} \quad \text{and} \quad x = 5 - \sqrt{7}
\]

Would you like further details or have any questions?

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Here are some related questions to deepen your understanding:
1. How would you solve the equation \(9(x + 3)^2 = 45\) using the square root property?
2. Can you use the square root property to solve \(2(x - 4)^2 = 18\)?
3. How would you isolate \((x + 2)^2\) in an equation like \(6(x + 2)^2 = 54\)?
4. What are the steps to solve an equation if you have a different coefficient in front of \((x - a)^2\)?
5. What happens if the equation results in a negative value under the square root?

**Tip:** When using the square root property, always remember to include both the positive and negative solutions!

Solve the quadratic equation using the square root property: 4(x−5)^2=28.

Learn how to solve the quadratic equation 4(x−5)^2=28 by isolating terms and applying the square root property. This detailed step-by-step solution explains key concepts in algebra and the square root property, suitable for students in Grades 8-10.

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