solve the quadratic equation 10x² - 2x + 13 = 3. which of the following expresses its solutions in the form…

Answer:

First, rewrite the quadratic equation (10x^{2}-2x + 13=3) as (10x^{2}-2x+10 = 0), then divide by 2 to get (5x^{2}-x + 5=0). Using the quadratic formula (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}) for (ax^{2}+bx + c = 0), here (a = 5), (b=-1), (c = 5). So (x=\frac{1\pm\sqrt{(-1)^{2}-4\times5\times5}}{2\times5}=\frac{1\pm\sqrt{1 - 100}}{10}=\frac{1\pm\sqrt{- 99}}{10}=\frac{1\pm3\sqrt{11}i}{10})

So the answer is (\frac{1}{10}\pm\frac{3\sqrt{11}}{10}i)