To solve the equation \( x^2 + 2x = 3 \), we first rearrange it into a standard form. We can do this by subtracting 3 from both sides:
\[ x^2 + 2x - 3 = 0 \]
Next, we will factor the quadratic equation. We need to find two numbers that multiply to \(-3\) (the constant term) and add to \(2\) (the coefficient of \(x\)). The numbers \(3\) and \(-1\) satisfy this condition, since:
\[ 3 \times (-1) = -3 \quad \text{and} \quad 3 + (-1) = 2 \]
Thus, we can factor the equation as follows:
\[ (x + 3)(x - 1) = 0 \]
To find the solutions, we set each factor equal to zero:
- \( x + 3 = 0 \) → \( x = -3 \)
- \( x - 1 = 0 \) → \( x = 1 \)
Therefore, the solutions to the equation \( x^2 + 2x = 3 \) are:
\[ x = -3, \quad x = 1 \]
Given the options provided, the correct answer is:
x = −3, 1