Solve the Quadratic Equation x² + 3x + 2 = 0 by Factoring

$x^2+3x+2=0$

To solve the quadratic equation $x^2 + 3x + 2 = 0$, we proceed as follows:

First, we identify that the equation is in standard form, where:

• $a = 1$
• $b = 3$
• $c = 2$

Next, we attempt to factor the quadratic equation. We look for two numbers that multiply to $ac = 1 \times 2 = 2$ and add up to $b = 3$. The numbers $2$ and $1$ satisfy these conditions because $2 \times 1 = 2$ and $2 + 1 = 3$.

Thus, we can factor the equation as:

$x^2 + 3x + 2 = (x + 2)(x + 1) = 0$

Now, we solve for $x$ by setting each factor equal to zero:

• $x + 2 = 0 \rightarrow x = -2$
• $x + 1 = 0 \rightarrow x = -1$

Therefore, the solutions to the quadratic equation are $x_1 = -2$ and $x_2 = -1$.

Since the problem is multiple-choice and we need to confirm the correct answer, we compare these solutions with the given choices. The correct choice is:

: $x_1=-2, x_2=-1$

Thus, the correct answer to the problem is:

\$x_1 = -2, x_2 = -1$