Solve the quadratic equation:

2x(squared)+6x+12=0

I know you have to find two numbers that =24 (2 times 12) and have a sum of 6. But I can't think of any! Can someone please help?

Use the quadratic.

And this problem has no real answers, they are imaginary.

Oh, the quadratic formula? Lol, why didn't I think of that?! Sorry, but thanks!!!

No problem! Let me help you solve the quadratic equation using the quadratic formula. The quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / (2a)

In your equation, let's compare it to the standard quadratic equation form, ax² + bx + c = 0:

a = 2
b = 6
c = 12

Substituting these values into the quadratic formula, we have:

x = (-6 ± √(6² - 4 * 2 * 12)) / (2 * 2)

Simplifying further:

x = (-6 ± √(36 - 96)) / 4
x = (-6 ± √(-60)) / 4

Here we encounter a problem: the value under the square root is negative. This means that the quadratic equation does not have any real solutions. Instead, it has two complex (imaginary) solutions. The square root of a negative number is represented as the imaginary unit "i," where i² = -1.

To simplify further, we can write the equation as:

x = (-6 ± 6i√10) / 4

Now, you can write the two complex solutions for x:

x = (-6 + 6i√10) / 4
x = (-6 - 6i√10) / 4

So the solutions to the quadratic equation 2x² + 6x + 12 = 0 are (-6 + 6i√10) / 4 and (-6 - 6i√10) / 4, which are complex numbers.