Question

Solve by completing the square method : 5y2 - 2y - 2=0​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A quadratic polynomial
• 5y²-2y-2=0

${\sf{\green{\underline{\large{To\:find}}}}}$

• Factors
• By completing squaring method

${\sf{\pink{\underline{\Large{Explanation}}}}}$

5y²-2y-2=0

multiplying by 5.

=>25y²-10y-10=0

=>(5y)²-2×5×1 +(1)² -(1)² -10 =0

=>(5y-1)²-1-10=0

=>(5y-1)²=11

=>5y-1=$\tt\pm\sqrt{11$

Taking x as +

=> 5y -1 =√11

=>5y = √11+1

=>y = (√11+1)/5

Taking as -

=> 5y -1 =-√11

=>5y = -√11+1

=>y = (-√11+1)/5

Answer 2

AnsweR

$\bold{5y^2-2y-2=0}$

Dividing by 5 , we get ,

$\implies \bold{\frac{5y^2}{5}-\frac{2y}{5}-\frac{2}{5}=0 }\\\\\implies \bold{y^2-\frac{2}{5}y-\frac{2}{5}=0 }\\\\\implies \bold{y^2-2.y.\frac{1}{5}- \frac{2}{5}=0 }$

Now add and subtracting (1/5)² on both sides , we get ,

$\implies \bold{y^2-2.y.\frac{1}{5}+(\frac{1}{5})^2-(\frac{1}{5} )^2-\frac{2}{5}=0 }\\\\\implies \bold{(y-\frac{1}{5} )^2=\frac{1}{25}+\frac{2}{5} }\\\\\implies \bold{(y-\frac{1}{5} )^2=\frac{(1+10)}{25} }\\\\\implies \bold{(y-\frac{1}{5} )^2=\frac{11}{25} }\\\\\implies \bold{(y-\frac{1}{5} )=\pm \frac{\sqrt{11}}{5} }\\\\\implies \bold{\bf{\blue{y=\frac{(1\pm\sqrt{11})}{5} }}}$