https://file.aiquickdraw.com/mathbot/file/17268431950181rq2uwa3.jpg

The quadratic equation given in the image is \( 6x^2 - 6 - 2x + 3x^2 - 1 = 0 \). First, let's combine like terms to simplify this equation:

\[
9x^2 - 2x - 7 = 0
\]

Now, we can solve for \( x \) using the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \( a = 9 \), \( b = -2 \), and \( c = -7 \). Substituting these values in, we calculate:
\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 9 \cdot (-7)}}{2 \cdot 9}
\]

\[
x = \frac{2 \pm \sqrt{4 + 252}}{18} = \frac{2 \pm \sqrt{256}}{18} = \frac{2 \pm 16}{18}
\]

This gives us the solutions:
\[
x_1 = \frac{2 + 16}{18} = 1, \quad x_2 = \frac{2 - 16}{18} = -\frac{14}{18} = -\frac{7}{9}
\]

Hence, the correct answer choice is \( x = 1 \) and \( x = -\frac{7}{9} \), which is not listed in the options provided in the image. This suggests that there may be a transcription error in the options or none of the provided answers are correct.

Would you like more detail on any step of the calculation or have other questions about quadratic equations?

**Further exploration questions:**
1. Would you like to review how to derive the quadratic formula?
2. Do you need help with a different quadratic equation?
3. Are you interested in understanding why the quadratic formula works for all quadratic equations?
4. Would you like to learn about completing the square, another method to solve quadratic equations?
5. Are you interested in exploring real-world applications of quadratic equations?

**Tip:** Always double-check the coefficients in your quadratic equation, as small errors can lead to incorrect solutions.

Solve the equation using the quadratic formula: -6x^2 - 6 - 2x + 3x^2 - 1 = 0

Learn how to solve the quadratic equation -6x^2 - 6 - 2x + 3x^2 - 1 = 0 using the quadratic formula. This detailed solution covers key algebraic concepts and is ideal for students in Grades 9-12.

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