Solve quadratic equation using square root method

To solve a quadratic equation using the square root method, the equation must be in the form:

\[ ax^2 + c = 0 \]

or

\[ x^2 = d \]

Here’s a step-by-step guide:

### Example Problem
Solve the equation:

\[ x^2 = 25 \]

### Steps to Solve Using the Square Root Method:

1. **Isolate the quadratic term**:  
   If the equation is not already in the form \( x^2 = d \), first rearrange it to isolate \( x^2 \). For instance:
   \[
   x^2 = 25
   \]

2. **Take the square root of both sides**:  
   Apply the square root to both sides of the equation:
   \[
   x = \pm\sqrt{25}
   \]

3. **Simplify the square root**:  
   Simplify the square root to find the possible values of \( x \):
   \[
   x = \pm 5
   \]

   So, the solutions are \( x = 5 \) and \( x = -5 \).

### Important Notes:
- The square root method only works directly when the quadratic equation has no linear term (i.e., no \( bx \) term) and the quadratic term is isolated.
- Always remember to consider both the positive and negative roots when taking the square root.

### Would you like to try this method on a specific equation?

### Follow-up Questions:
1. What is the first step in solving \( 4x^2 = 36 \) using the square root method?
2. How would you solve \( x^2 = -9 \) using this method? (Hint: Consider complex numbers.)
3. Can the square root method be used to solve \( x^2 + 6x + 9 = 0 \)?
4. How does the square root method differ from factoring in solving quadratic equations?
5. What are the limitations of the square root method?

### Tip:
Always double-check that the quadratic term is isolated before applying the square root method.

Learn how to solve quadratic equations using the square root method with a detailed step-by-step guide. Includes examples and explanations of isolating the quadratic term and applying the square root operation. Suitable for high school students.

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