https://file.aiquickdraw.com/mathbot/file/17289892684027fg2efae.jpg

The equation provided in the image is:

\[
3x^2 = -x + 8
\]

We can rewrite this equation in standard quadratic form:

\[
3x^2 + x - 8 = 0
\]

Now we can use the **quadratic formula** to solve for \(x\):

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

Where \(a = 3\), \(b = 1\), and \(c = -8\). Substituting these values into the quadratic formula:

\[
x = \frac{-1 \pm \sqrt{1^2 - 4(3)(-8)}}{2(3)}
\]

Simplifying the discriminant:

\[
x = \frac{-1 \pm \sqrt{1 + 96}}{6}
\]
\[
x = \frac{-1 \pm \sqrt{97}}{6}
\]

Taking the square root of 97:

\[
x = \frac{-1 \pm 9.85}{6}
\]

Now solving for the two possible solutions:

1. \(x_1 = \frac{-1 + 9.85}{6} = \frac{8.85}{6} \approx 1.475\)
2. \(x_2 = \frac{-1 - 9.85}{6} = \frac{-10.85}{6} \approx -1.808\)

Thus, the solutions to the equation are:

\[
x \approx 1.48, -1.81
\]

Would you like a detailed explanation or further steps? 

Here are some follow-up questions related to this:

1. How is the discriminant used in determining the nature of the roots of a quadratic equation?
2. Can you explain the steps involved in simplifying the quadratic formula?
3. How do you estimate square roots like \(\sqrt{97}\)?
4. Why does the quadratic equation often yield two solutions?
5. Can you solve this same equation using factoring instead of the quadratic formula?

**Tip:** Always check the discriminant first, as it can help you determine whether there are real or complex solutions.

Use the quadratic formula to solve for x: 3x^2 = -x + 8. Round your answer to the nearest hundredth.

Learn how to solve the quadratic equation 3x^2 = -x + 8 using the quadratic formula. This problem covers key algebraic concepts, including the quadratic equation formula and simplifying steps. Suitable for students in Grades 8-10.

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