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enot [183]
4 years ago
5

Solve equation y^2+3y=-1​

Mathematics
1 answer:
Kipish [7]4 years ago
8 0

y =  \frac{ \sqrt{13} - 3}{2}

Answer:

y =  \frac{ - \sqrt{13} - 3}{2}

Step-by-step explanation:

{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} }}}

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