Question

the root of equation
$5x{2} - 6x - 2 = 0$
by method of completing the square

Answer 1

.........answer..........

Answer 2

Solution :-

The given quadratic equation is 5x² - 6x - 2 = 0

Multiplying both sides by 5, we get.

25x² - 30x - 10 = 0

Or, (5x)² - (2*5x*3) + (3)² - (3)² - 10 = 0

⇒ (5x - 3)² - 9 - 10 = 0

⇒ (5x - 3)² = 19 

⇒ 5x - 3 = + √19  or 5x - 3 = - √19

⇒ 5x = 3 + √19  Or 5x = 3 - √19

⇒ x = (3 + √19)/5  Or x = (3 - √19)/5

So, (3 + √19)/5 Or (3 - √19)/5 are the roots of the given equation.