Solving Quadratic Equations by Completing Square
Sometimes factorization of a given quadratic equation is not possible. When coefficients in the quadratic equation are large numbers, then it may be difficult to factorize. In this case, we can use the completing square method.
In order to solve the quadratic equation with the completing square method, we have the following steps:

Write the equation in standard form.

Shift the constant term on RHS.

Make the coefficient of as one.

Add on both sides

Finally, simplify the equation to get the required roots.
Example:
Solve the equation by the completing square method.
Solution:
Write the equation in standard form
Shifting the constant term on RHS, we get
Make the coefficient of as and divide the equation by
Now adding to both sides, we get
Taking the square root of both sides, we get
Either
or
Example:
Solve the equation by the completing square method.
Solution:
Write the equation in standard form as
Multiply by to make the coefficient of positive
Shifting the constant term on RHS, we get
Now adding to both sides, we get
Taking the square root of both sides, we get
Either or