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.