solve equation by the quadratic formula. list the solutions, separated by commas. 4k² - k + 3 = 2 k =

Explanation:

Step1: Rewrite in standard form

First, rewrite $4k^{2}-k + 3=2$ as $4k^{2}-k+1 = 0$. Here, $a = 4$, $b=-1$, $c = 1$.

Step2: Apply quadratic formula

The quadratic formula is $k=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 4$, $b=-1$, $c = 1$ into it: [ \begin{align*} k&=\frac{-(-1)\pm\sqrt{(-1)^{2}-4\times4\times1}}{2\times4}\ &=\frac{1\pm\sqrt{1 - 16}}{8}\ &=\frac{1\pm\sqrt{- 15}}{8}\ &=\frac{1\pm i\sqrt{15}}{8} \end{align*} ]

Answer:

$\frac{1 + i\sqrt{15}}{8},\frac{1 - i\sqrt{15}}{8}$