Question

What are the possible values of x in x2 + 3x + 3 = 0?

Answer 1

Answer:

Step-by-step explanation:

The answer is C. `(-3 stackrel(+)(-) isqrt(3))/(2)`

Answer 2

To solve a quadratic equation like $ax^2+bx+c=0$, you can use the quadratic formula

$x_{1,2} = \cfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

In your case, $a = 1, b = c = 3$, so the formula becomes

$x_{1,2} = \cfrac{-3\pm\sqrt{(-3)^2-4\cdot 1\cdot 3}}{2\cdot 1}$

We can simplify the expression:

$x_{1,2} = \cfrac{-3\pm\sqrt{9-12}}{2} = \cfrac{-3\pm\sqrt{-3}}{2}$

Since -3 is negative, its square root is computed as

$\sqrt{-3} = \sqrt{-1\cdot 3} = \sqrt{-1}\sqrt{3} = \sqrt{3}i$

So, the solutions are

$x = \cfrac{-3+i\sqrt{3}}{2} \text{ or } x = \cfrac{-3-i\sqrt{3}}{2}$