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

Now in the above quadratic equation the coefficient of x² is 4. Let us make it unity by dividing the entire quadratic equation by 4.

x² + √3x + 3/4 = 0

x² + √3x = -3/4

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

Coefficient of x = √3

Half of √3= √3/2

Squaring the half of √3= 3/4

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 = √3/2

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

(x ± A)² = k²

Here RHS term is zero which implies that the roots of the quadratic equation are real and equal.

Taking square root of both sides,