Solve the following quadratic equations by the method of completing the square:

5x² – 6x – 2 = 0

Now in the above quadratic equation the coefficient of x² is 5. Let us make it unity by dividing the entire quadratic equation by 5.

x² – 6/5x - 2/5 = 0

x² – 6/5x = 2/5

Now by taking half of the coefficient of x and then squaring it and adding on both LHS and RHS sides.

Coefficient of x = 6/5

Half of 6/5 = 6/10

Squaring the half of 6/10 = 36/100

Now the LHS term is a perfect square and can be expressed in the form of (a-b) ² = a² – 2ab + b² where a = x and b = 6/10

On simplifying both RHS and LHS we get an equation of following form,

(x ± A)² = k²

Taking Square root of both sides.

Now taking the positive part,

Now taking the negative part,

Now taking the positive part,