The solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -3 and x = -2.

Answer 1

You're correct! The solutions to the quadratic equation $x^2+5x+6=0$ can be found by factoring the equation.

The quadratic can be factored as:

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

Setting each factor equal to zero gives us the solutions:

1. $x+2=0$ leads to $x=-2$
2. $x+3=0$ leads to $x=-3$

Thus, the solutions are indeed $x=-3$ and $x=-2$.

You can also verify the solutions by using the quadratic formula:

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

For this specific equation:

• $a=1$
• $b=5$
• $c=6$

Plugging in these values:

$$x=\frac{-5\pm \sqrt{5^2-4\cdot 1\cdot 6}}{2\cdot 1}$$ $$x=\frac{-5\pm \sqrt{25-24}}{2}$$ $$x=\frac{-5\pm 1}{2}$$

This gives the two solutions:

1. $x=\frac{-5+1}{2}=\frac{-4}{2}=-2$
2. $x=\frac{-5-1}{2}=\frac{-6}{2}=-3$

So, both methods confirm that the solutions are $x=-3$ and $x=-2$.