https://file.aiquickdraw.com/mathbot/file/1728932887139t5a0tvbw.jpg

The quadratic equation shown in the image is:

\[
x^2 - 6x - 36 = 0
\]

To solve this, we can use the **quadratic formula**:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \(x^2 - 6x - 36 = 0\), the coefficients are:
- \(a = 1\)
- \(b = -6\)
- \(c = -36\)

Now substitute these values into the quadratic formula:

\[
x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-36)}}{2(1)}
\]

Simplifying step by step:
1. \(x = \frac{6 \pm \sqrt{36 + 144}}{2}\)
2. \(x = \frac{6 \pm \sqrt{180}}{2}\)
3. \(x = \frac{6 \pm \sqrt{36 \times 5}}{2}\)
4. \(x = \frac{6 \pm 6\sqrt{5}}{2}\)

Finally, simplify:

\[
x = 3 \pm 3\sqrt{5}
\]

Thus, the two solutions are:

\[
x = 3 + 3\sqrt{5} \quad \text{and} \quad x = 3 - 3\sqrt{5}
\]

Let me know if you'd like any clarifications or further details!

Here are five related questions:
1. How do you factor a quadratic equation manually?
2. What does the discriminant in a quadratic equation tell us about the number of real solutions?
3. Can you solve this equation by completing the square instead of using the quadratic formula?
4. How do you graph a quadratic equation, and what does the graph look like for this equation?
5. What are the possible applications of quadratic equations in real-world problems?

**Tip:** When solving a quadratic equation, always check if it's factorable before using the quadratic formula—it can save time!

Solve the quadratic equation: x^2 - 6x - 36 = 0

Learn how to solve the quadratic equation x^2 - 6x - 36 using the quadratic formula. This step-by-step guide covers key algebra concepts and shows how to simplify the square roots. Suitable for students in Grades 9-12.

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