For this case we have the following quadratic equation:
[tex]x ^ 2-4x + 23 = 0[/tex]
The solutions will be given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Where:
[tex]a = 1\\b = -4\\c = 23[/tex]
Substituting the values we have:
[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (23)}} {2 (1)}\\x = \frac {4 \pm \sqrt {16-92}} {2}\\x = \frac {4 \pm \sqrt {-76}} {2}\\x = \frac {4 \pm \sqrt {76i ^ 2}} {2}\\x = \frac {4 \pmi \sqrt {76}} {2}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 19}} {2}\\x = \frac {4 \pm2i \sqrt {19}} {2}\\x = 2 \pm i\sqrt {19}[/tex]
We have two roots:
[tex]x_ {1} = 2-i \sqrt {19}\\x_ {2} = 2 + i \sqrt {19}[/tex]
ANswer:
[tex]x_ {1} = 2-i\sqrt {19}\\x_ {2} = 2 + i\sqrt {19}[/tex]
