Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.
x= 3+√195
Multiplying the equation throughout by 5, we get
25 x2– 30 x – 10= 0
This is the same as
(5x)2−2×5x×3+32−32−10=0
⇒ (5x−3)2 - 9 - 10 = 0
⇒ (5x−3)2 - 19 = 0
⇒ (5x−3)2 = 19
⇒ 5x - 3 = ±√19
⇒ 5x = 3±√19
⇒ x = 3±√195
Therefore, the roots are 3+√195 and 3−√195.
Since √19>3, 3−√195 will be negative.
Thus, the positive root is 3+√195.