Question

What is the solution?. 1/2x2 – x + 5 = 0

Answer 1

1/2 x^2 - x + 5 = 0
Multiply through by 2 to get:
x^2 - 2x + 10 = 0
$x= \frac{-b\pm\sqrt{b^2-4ac}}{2a}$; where a = 1, b = -2 and c = 10
$x=\frac{-(-2)\pm\sqrt{(-2)^2-(4\times1\times10)}}{2\times1}\\=\frac{2\pm\sqrt{4-40}}{2}\\=\frac{2\pm\sqrt{-36}}{2}\\=\frac{2\pm6i}{2}\\=1\pm3i$
Therefore, x = 1 + 3i or x = 1 - 3i