[tex] {x}^{2} + 5x + 3 = 0 \\ {(x)}^{2} + 2(x)( \frac{5}{2} ) + {( \frac{5}{2} })^{2} - \frac{13}{4} = 0 \\ ( {x + \frac{5}{2} })^{2} - \frac{13}{4} = 0 \\ ( {x + \frac{5}{2} })^{2} - {(\frac{ \sqrt{13} }{2})}^{2} = 0 \\ (x + \frac{5}{2} + \frac{ \sqrt{13} }{2} )(x + \frac{5}{2} - \frac{ \sqrt{13} }{2} ) = 0 \\ (x + \frac{5 + \sqrt{13} }{2})(x + \frac{5 - \sqrt{13} }{2} ) = 0\\ so \: x = \frac{-5 - \sqrt{13} }{2} \: or \: x = \frac{ - 5 + \sqrt{13} }{2} [/tex]
the answer is the second one
