To solve the equation \( x^2 + 2x = 3 \), we first rewrite it in standard form:
\[ x^2 + 2x - 3 = 0 \]
Next, we can plot the function defined by the left-hand side of the equation:
\[ f(x) = x^2 + 2x - 3 \]
To find the roots of the equation, we can either graph the function \( f(x) \) or factor it. In this case, let's factor the quadratic expression.
We need to find two numbers that multiply to \(-3\) (the constant term) and add to \(2\) (the coefficient of \(x\)). The numbers that fit these criteria are \(3\) and \(-1\):
\[ x^2 + 2x - 3 = (x + 3)(x - 1) = 0 \]
Setting each factor equal to zero gives us the solutions:
- \( x + 3 = 0 \) ⇒ \( x = -3 \)
- \( x - 1 = 0 \) ⇒ \( x = 1 \)
Thus, the solutions to the equation \( x^2 + 2x = 3 \) are:
\[ x = -3, , 1 \]
From your response options, the correct answer is:
x = -3, 1