Question

2y2+9y+10=0 completing square method

Answer 1

$\frac{ {2y}^{2} }{2} + \frac{9y}{2} + \frac{10}{2} = 0 \\ \\ {y}^{2} + \frac{9y}{2} + 5 = 0 \\ \\ {y}^{2} + 2 \times y \times \frac{9}{4} + (\frac{9}{4})^{2} - ( \frac{9}{4})^{2} + 5 = 0 \\ \\ (y + \frac{9}{4} )^{2} - ( \frac{9}{4})^{2} + 5 =0 \\ \\ (y + \frac{9}{4} )^{2} - \frac{81}{16} + 5 = 0 \\ \\ (y + \frac{9}{4} )^{2} - \frac{81 - 80}{16} = 0 \\ \\ (y + \frac{9}{4} )^{2} - \frac{1}{16} = 0 \\ \\ (y + \frac{9}{4} )^{2} = \frac{1}{16} \\ \\ y + \frac{9}{4} = \sqrt{ \frac{1}{16} } \\ \\ y + \frac{9}{4} = (+ )( - )\frac {1}{4} \\ \\ y =( + ) \frac {1}{4} - \frac{9}{4} \\ \\ y = \frac{ - 8}{4} \\ \\ y = - 2 \\ \\ y = ( - ) \frac{1}{4} - \frac{9}{4} \\ \\ y = - \frac{10}{4} = - \frac{5}{2}$
Hope this helps!