Solve the equation for *all values* of x*x*.

49, x, squared, minus, 144, equals, 0

49*x*2−144=

0

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.

Solve the equation for all values of x: 49x^2 - 144 = 0

Learn how to solve the quadratic equation 49x^2 - 144 = 0 step by step. This problem introduces algebraic concepts such as solving quadratic equations using the square root method. Suitable for students in Grades 8-10.

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