Question

Explain the method of completing the square and ans this

$5 x^{2} -6x-2$

Answer 1

step 1:  x²-6/5 x -2/5 = 0 divding equation with 5
step 2 : x²-6x/5 = 2/5
step 3: x²-6x/5 + (3/5)² = 2/5 +(3/5)²     adding (3/5)² on both sides
step 4: (x- 3/5)² = 2/5 + 9/25
step 5: (x- 3/5)² = 19/25
step 6: x-3/5=√19/√25
step 7: x = 3/5+√19/5
so x = 3+√19/5
s0 x = 3+√19/5 or 3-√19/5
this is the completing square method

Answer 2

Completing the square:
The method is used to solve a quadratic equation,
The following steps  to solve the given equation will make you understand it:

STEP 1:
=0
As the name suggests, we need to complete the squares in it,
So in
5x²-6x-2=0
divide the middle term by 2 and square the quotient so in here we get

5x²-6x+(3)²-2=0+9

we add 9 on the other so that there is no increments or decrements  in the equation , 

STEP 2:
Now you would see that
5x²-6x+(3)²-2=0+9  

=>  5x²-6x+(3)² = 9+2

=> 5x²-6x+(3)² = 11

  Divide the equation by 5 (both side , so that the first term's coefficient  becomes 1. 

This gives   x²- frac{6}{5} x+( frac{9}{5} ) =   frac{11}{5} 
 x²- frac{6}{5} x+( frac{9}{5} ) forms an identity i.e. (a-b)²=a²-2ab+b²

So using the identity we form it as;

(x-3)²=11/5

so x=3+√11/5  or  3-√11/5


$\frac{11}{5}$