Create a function graph to answer the question. Use the function graph to solve for the solutions to the equation x2+2x=3

Question

.(1 point)
Responses

x=2,0
x equals 2 comma 0

x=0,1
x equals 0 comma 1

x=−3,1
x equals negative 3 comma 1

no solution

Answer 1

To solve the equation \(x^2 + 2x = 3\), we can first rewrite it in standard form:

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

Next, we can factor this quadratic equation. We need to find two numbers that multiply to \(-3\) (the constant term) and add up to \(2\) (the coefficient of the linear term).

The factors of \(-3\) that meet these criteria are \(3\) and \(-1\). Therefore, we can factor the equation as follows:

\[ (x + 3)(x - 1) = 0 \]

Setting each factor to zero gives the solutions:

1. \(x + 3 = 0 \quad \Rightarrow \quad x = -3\)
2. \(x - 1 = 0 \quad \Rightarrow \quad x = 1\)

So, the solutions to the equation \(x^2 + 2x = 3\) are:

\[ x = -3 \quad \text{and} \quad x = 1 \]

Now we can summarize this in a response format:

Response: \( x = -3, 1 \) (or "x equals negative 3 comma 1")