Convert a quadratic expression to completed square form by following these steps:
 Start with the quadratic expression in standard form, i.e. with the terms in the order:
quadratic, linear, constant:
a x^{ 2} + b x + c
 If the leading coefficient (i.e. the coefficient of the
quadratic term) is not equal to 1 then factor it out.
This may produce fractions in the linear and constant terms but
the important thing is to get a leading coefficient of 1 inside the brackets:
 From now on we ignore the factor outside the brackets and continue working
on the quadratic trinomial inside the brackets.
Take the coefficient of the linear term (namely b/a),
divide it by 2, and then square it.
This produces the quantity .
 Add and immediately subtract back off the quantity
inside the brackets, right after the linear term, like this:
 Use brackets to group the first three terms inside the brackets:
The purpose of adding
to this group was to make this group a perfect square.
But to keep the value of the entire expression unchanged,
the rest had to have
subtracted from it.
 Write the perfect square in factored form:
 Write “the rest” as a single fraction.
The result is the socalled completed square form:
