What are the solutions?

1/2x^2+2x+3=0

chuck the fraction:

x^2 + 4x + 6 = 0

x = -2 ± i√2

hek you

To find the solutions to the equation 1/2x^2 + 2x + 3 = 0, we can use the quadratic formula.

The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 1/2, b = 2, and c = 3. Plugging in these values, we can calculate the solutions as follows:

x = ( -2 ± √(2^2 - 4(1/2)(3)) ) / (2 * (1/2))
x = ( -2 ± √(4 - 6) ) / 1
x = ( -2 ± √(-2) ) / 1

The discriminant (the part inside the square root) is negative (-2), which means that the equation has no real solutions. The solutions are complex numbers.

To express the solutions in terms of complex numbers, we can simplify the square root of -2. By convention, we use the imaginary unit i, where i^2 = -1.

√(-2) = √(2 * -1) = √(2) * √(-1) = i√2

Therefore, the solutions are:

x = ( -2 + i√2 ) / 1
x = ( -2 - i√2 ) / 1

In simpler terms, the solutions are:

x = -2 + i√2
x = -2 - i√2