[tex] y = \frac{ \sqrt{13} - 3}{2}[/tex]
Answer:
[tex] y = \frac{ - \sqrt{13} - 3}{2}[/tex]
Step-by-step explanation:
[tex] {y}^{2} + 3y = - 1 \\ {y}^{2} + 3y + 1 = 0 \\ {y}^{2} + 2. \frac{3}{2} y + \bigg( \frac{3}{2} \bigg)^{2} - \bigg( \frac{3}{2} \bigg)^{2} - 1 = 0 \\ \bigg( {y} + \frac{3}{2} \bigg)^{2} - \frac{9}{4} - 1 = 0 \\ \bigg( {y} + \frac{3}{2} \bigg)^{2} - \frac{9 - 4}{4} = 0 \\ \bigg( {y} + \frac{3}{2} \bigg)^{2} - \frac{13}{4} = 0 \\ \bigg( {y} + \frac{3}{2} \bigg)^{2} = \frac{13}{4} \\ {y} + \frac{3}{2} = \pm\frac{ \sqrt{13}}{2} \\ y = \pm\frac{ \sqrt{13}}{2} - \frac{3}{2} \\ y = \pm\frac{ \sqrt{13} - 3}{2} \\ \red{ \boxed{ \bold{y = \frac{ \sqrt{13} - 3}{2}}}} \: or \: \purple{ \boxed{ \bold{ y = \frac{ - \sqrt{13} - 3}{2} }}}[/tex]
