Question

y²-8y+180=0 ( by completing the square method)

Answer 1

${y}^{2} - 8y + 180 = 0$
it is in the form of ay^2 + by+ c = 0
here a= 1 , b = -8 , c = 180
by completing square method
divide both sides with 'a' i.e.,1
the result will be
${y}^{2} - 8y + 180 = 0$
send 'c' i.e., 180 to R. H. S
y^2 - 8y = -180
now add the following on both sides
$(b {}^{2} \div 2a) {}^{2} = ( - 8 \div 2 \times 1) = ( - 8 \div 2) {}^{2}$
y^2 - 8y + (-8/2)^2 = -180 + (-8/2)^2
now LHS is in the form of :
$a { }^{2} + b {}^{2} - 2ab =( a - b) {}^{2}$
( y - 8/2)^2 = -180 + 64/4
( y - 8/2 ) ^2 = -180 + 16
( y - 8/2 ) ^2 = - 164
$y - 4 = \sqrt{ - 164}$
y - 4 = 12.8
y = 12.8 + 4
y = 16. 8

therefore, y = + 16.8 or - 16.8

hope it helps....

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