Question

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

Answer 1

Answer:

8i and -8i

Step-by-step explanation:

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

$\frac{1}{2}(x^2+40)=-12\\\frac{1}{2}x^2+20=-12\\\frac{1}{2}x^2+32=0$

Solve for x using the quadratic formula:

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

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