x² + 2x + 3 =0
use the quadratic formula
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Step-by-step explanation:
[tex]x = \frac{ - b ( + - ) \sqrt{ {b}^{2} - 4ac } }{2a} \\ x1 = \frac{ - 2 + \sqrt{ {2}^{2} - 4(1)(3)} }{2(1)} \\ = \frac{ - 2 + \sqrt{4 - 12} }{2} \\ = \frac{ - 2 + \sqrt{ - 8} }{2} \\ = \frac{ - 2 + \sqrt{(4)( - 2)} }{2} \\ = \frac{ - 2 + 2 \sqrt{2}i }{2} [/tex]
[tex]x2 = \frac{ - 2 - 2 \sqrt{2} i}{2} [/tex]