https://file.aiquickdraw.com/mathbot/file/17255640168391gmw3l37.jpg

The problem in the image is asking to solve the quadratic equation:

\[
x^2 + 3x = 10
\]

To solve this quadratic equation, let's rearrange it into standard form:

\[
x^2 + 3x - 10 = 0
\]

Now we can use the quadratic formula:

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

In this case, \(a = 1\), \(b = 3\), and \(c = -10\). Plugging these values into the formula:

\[
x = \frac{-3 \pm \sqrt{3^2 - 4(1)(-10)}}{2(1)}
\]

\[
x = \frac{-3 \pm \sqrt{9 + 40}}{2}
\]

\[
x = \frac{-3 \pm \sqrt{49}}{2}
\]

\[
x = \frac{-3 \pm 7}{2}
\]

Now we solve for both possible values of \(x\):

1. \(x_1 = \frac{-3 + 7}{2} = \frac{4}{2} = 2\)
2. \(x_2 = \frac{-3 - 7}{2} = \frac{-10}{2} = -5\)

Thus, the solutions are \(x = 2\) and \(x = -5\).

The correct answer is:

\[
x = 2 \text{ and } x = -5
\]

This corresponds to the second option in the image.

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Would you like more details or have any questions about this solution? Here are some related questions to expand your understanding:

1. How does completing the square compare to using the quadratic formula for solving this problem?
2. Can all quadratic equations be solved using the quadratic formula?
3. What does the discriminant \(b^2 - 4ac\) tell you about the solutions of a quadratic equation?
4. How do you factor the quadratic equation \(x^2 + 3x - 10 = 0\)?
5. How can you graphically verify the solutions of the quadratic equation?

**Tip**: The quadratic formula works for any quadratic equation, but factoring might give you quicker results if the equation is factorable.

Solve the quadratic equation x^2 + 3x = 10.

Learn how to solve the quadratic equation x^2 + 3x = 10 with a detailed step-by-step guide. This problem involves using the quadratic formula to find the solutions, appropriate for students in Grades 9-11.

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