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Question
`5x^2-6x-2=0`
Solution
`5x^2-6x-2=0`
⇒`25x^2-30x-10=0`
⇒`25x^2-30x=10`
⇒`(5x)^2-xx5x xx3+3^2=10+3^3` (Adding `3^2` on both sides)
⇒`(5x-3)^2=10+9-19`
⇒`5x-3=+-sqrt19` (Taking square root on both)
⇒`5x-3=sqrt19 or 5x-3=-sqrt19`
⇒`5x=3+-sqrt19 or 5x=3-sqrt19`
⇒`x=(3+sqrt19)/5 or x=(3-sqrt19)/5`
Hence, `(3+sqrt19)/5` and `(3-sqrt19)/5` are `(3-sqrt19)/5` are the roots of the given equation.
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