The equation you've provided is:

$49x^2 - 144 = 0$

Let's solve for $x$:

Step 1: Add 144 to both sides of the equation:

$49x^2 = 144$

Step 2: Divide both sides by 49:

$x^2 = \frac{144}{49}$ $x^2 = \left(\frac{12}{7}\right)^2$

Step 3: Take the square root of both sides:

$x = \pm \frac{12}{7}$

Solution:

The values of $x$ are:

$x = \frac{12}{7} \quad \text{or} \quad x = -\frac{12}{7}$

Do you need further clarification or any details? Here are 5 follow-up questions:

1. How would you solve a similar equation with different coefficients?
2. What happens if the equation includes a linear term (like $49x^2 + 5x - 144 = 0$)?
3. Can you solve this equation using a different method, such as factoring?
4. How would you graph the function $f(x) = 49x^2 - 144$?
5. What is the significance of the ± sign when solving quadratic equations?

Tip: Remember, when solving quadratic equations, always check if they can be simplified or factored before using the quadratic formula or square root methods.