Question

Completing square method :5x^2-6x-5=0

Answer 1

first... divide the equation by 5....
then,
we get

x^2-6/5x-1=0

if x^2-6/5x+k=(x+a)^2

then, x^2-6/5x+k=x^2+2ax+a^2

compare....-6/5x+k & 2ax+a^2

then....
2a=-6/5
a=-6/10
a= -3/5

k=a^2
k= (-3/5)^2=9/25

now....here is ur equation

x^2-6/5x+9/25-9/25-1=0
(x-3/5)^2-9-25/25=0

x-3/5^2 -36/25=0
(x-3/5)^2=36/25

$(x - \frac{3}{5} ) = \sqrt{ \frac{36}{25} } \\ (x - \frac{3}{5} ) = \frac{6}{5} \\ x = \frac{6}{5} + \frac{3}{5} \: \: \: or \: \: x = - \frac{6}{5} + \frac{3}{5} \\ x = \frac{9}{5} \: \: \: \: or \: \: \: x = \frac{ - 3}{5}$
hence these are ur roots. of equation...
mark as best....