Question

Solve by quadratic formula or completion of square

$18. \: y {}^{2} + 77 - 18y = 0$

Standard:- 10

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Answer 1

y²+77-18y=0

y²+77-11y-7y=0

y²-11y+77-7y=0

y(y-11)-7(-11+y)=0

(y-7)(y-11)=0

y=7 or 11

Answer 2

Completion of square method:

Given Equation is y^2 - 18y + 77 = 0

= > y^2 - 18y + 77 = 0

Add and subtract (9)^2, we get

= > y^2 - 18y + 77 + (9)^2 - (9)^2 = 0

= > y^2 - 18y + (9)^2 + 77 - (9)^2 = 0

= > (y - 9)^2 + 77 - (9)^2 = 0

= > (y - 9)^2 = (9)^2 - 77

= > (y - 9)^2 = 81 - 77

= > (y - 9)^2 = 4.

= > (y - 9) = +2, -2


(1)

= > y - 9 = 2

= > y = 2 + 9

= > y = 11.



(2) 

= > y - 9 = -2

= > y = -2 + 9

= > y = 7.



Therefore the values of y = 11, 7.



Hope this helps!