Question

Solve equation y^2+3y=-1​

Answer 1

`y = ( √(13) - 3)/(2)`

Answer:

`y = ( - √(13) - 3)/(2)`

Explanation:

`{y}^(2) + 3y = - 1 \\ {y}^(2) + 3y + 1 = 0 \\ {y}^(2) + 2. (3)/(2) y + \bigg( (3)/(2) \bigg)^(2) - \bigg( (3)/(2) \bigg)^(2) - 1 = 0 \\ \bigg( {y} + (3)/(2) \bigg)^(2) - (9)/(4) - 1 = 0 \\ \bigg( {y} + (3)/(2) \bigg)^(2) - (9 - 4)/(4) = 0 \\ \bigg( {y} + (3)/(2) \bigg)^(2) - (13)/(4) = 0 \\ \bigg( {y} + (3)/(2) \bigg)^(2) = (13)/(4) \\ {y} + (3)/(2) = \pm( √(13))/(2) \\ y = \pm( √(13))/(2) - (3)/(2) \\ y = \pm( √(13) - 3)/(2) \\ \red{ \boxed{ \bold{y = ( √(13) - 3)/(2)}}} \: or \: \purple{ \boxed{ \bold{ y = ( - √(13) - 3)/(2) }}}`