Question

Solve the equation for Imaginary Numbers 1/2(x^2+40)=-12

Answer 1

8i and -8i

Explanation:

Move everything into the left-hand side to get a quadratic equation:

`(1)/(2)(x^2+40)=-12\\(1)/(2)x^2+20=-12\\(1)/(2)x^2+32=0`

Solve for x using the quadratic formula:

`(1)/(2)x^2+32=0\\x=(-b\±√(b^2-4ac))/(2a)\\x=\frac{-(0)\±\sqrt{0^2-4((1)/(2))32}}{2((1)/(2))}\\x=\±√(-64)\\x=\±8i`

The two imaginary solutions for the equation are 8i and -8i.