Question

${y}^{2} + \frac{9}{2} y + 5 = 0$
Solve using completing square method.
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Answer 1

Answer:

$y^2+\frac{9}{2}y+5=0\\\\ y^2+2.y.\frac{9}{4}+5=0$

Now compare middle term with 2ab we will get ,

b = 9/4

Now add and subtract  (9/4)² , we will get ,

$=>y^2+2.y.\frac{9}{4}+(\frac{9}{4} )^2-(\frac{9}{4} )^2+5=0$

Now first three terms in the expression is in the form a²+2ab+b².

$=>(y+\frac{9}{2} )^2-\frac{81}{16}+5=0\\\\ =>(y+\frac{9}{2} )^2=\frac{81}{16}-5\\\\=>(y+\frac{9}{2} )^2=\frac{81-80}{16}\\\\ =>(y+\frac{9}{2} )^2=\frac{1}{16}\\\\ =>y+\frac{9}{2} =\pm \frac{1}{4}\\\\\ =>y=\frac{1}{4}-\frac{9}{2} \:\:\:,\:\:\: y=-\frac{1}{4}-\frac{9}{2}\\\\=> y=\frac{-17}{4}\:\:\:,\:\:\:y=\frac{-19}{4}$