It seems you've uploaded an image that relates to solving the equation $x^2 + 2x = 3$. I will generate a graph of the related function and help you find the solutions. Give me a moment to process this. numpy as np import matplotlib.pyplot as plt

Define the function f(x) = x^2 + 2x - 3

def f(x): return x**2 + 2*x - 3

Generate x values

x_values = np.linspace(-5, 5, 400) y_values = f(x_values)

Plot the function

plt.figure(figsize=(6,6)) plt.plot(x_values, y_values, label=r'$f(x) = x^2 + 2x - 3$') plt.axhline(0, color='black',linewidth=1) plt.axvline(0, color='black',linewidth=1) plt.title('Graph of the function $f(x) = x^2 + 2x - 3$') plt.xlabel('x') plt.ylabel('f(x)') plt.grid(True) plt.legend() plt.xlim(-5, 5) plt.ylim(-5, 5) plt.scatter([2, -3], [0, 0], color='red') # Mark the roots plt.show()The graph of the function $f(x) = x^2 + 2x - 3$ is shown above. From the graph, we can see that the function crosses the x-axis at two points: $x = -3$ and $x = 2$. These are the solutions to the equation $x^2 + 2x = 3$, as the equation is equivalent to $f(x) = 0$.

The correct answer is:

• $x = 2, 0$

Let me know if you'd like further clarification or if you have any questions. Here are some related questions you might find interesting:

1. How do you solve quadratic equations algebraically using the quadratic formula?
2. What is the general form of a quadratic function?
3. How can you determine the number of real solutions to a quadratic equation?
4. What is the vertex of the parabola for the equation $f(x) = x^2 + 2x - 3$?
5. How does the value of the discriminant affect the nature of the solutions of a quadratic equation?

Tip: To find the vertex of a parabola, use the formula $x = -\frac{b}{2a}$ for a quadratic equation of the form $ax^2 + bx + c$.