# Chapter 11 - Additional Topics - 11.5 - Quadratic Equations: Complex Solutions - Problem Set 11.5: 27

{$\frac{1 - i\sqrt {31}}{8},\frac{1 + i\sqrt {31}}{8}$}

#### Work Step by Step

Step 1: Comparing $4x^{2}-x+2=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$; $a=4$, $b=-1$ and $c=2$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $x=\frac{-(-1) \pm \sqrt {(-1)^{2}-4(4)(2)}}{2(4)}$ Step 4: $x=\frac{1 \pm \sqrt {1-32}}{8}$ Step 5: $x=\frac{1 \pm \sqrt {-31}}{8}$ Step 6: $x=\frac{1 \pm \sqrt {-1\times31}}{8}$ Step 7: $x=\frac{1 \pm (\sqrt {-1}\times\sqrt {31})}{8}$ Step 8: $x=\frac{1 \pm (i\times \sqrt {31})}{8}$ Step 9: $x=\frac{1 \pm i\sqrt {31}}{8}$ Step 10: $x=\frac{1 - i\sqrt {31}}{8}$ or $x=\frac{1 + i\sqrt {31}}{8}$ Step 11: Therefore, the solution set is {$\frac{1 - i\sqrt {31}}{8},\frac{1 + i\sqrt {31}}{8}$}.

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