# Completion of square

Solve the given equations by completing squares. *Please explain every single step for me.*

Solve the given equations by completing squares. Please explain every single step for me.

Rajni
Sahsah.rajni@yahoo.comAdministratorSOLVE - ΜΔΓΗŠ
Let us start with the third equation .

We try factorizing the given quadraic equations first. If the resulting factors are same, we get the equation in square form. So no special method is required.

Now, the most basic method of factorizing any quadratic equation(if it is factorizable) follows the given steps :

a) arrange the terms in descending powers of x. (Consider it of the form

b) consider the coeffient of the ‘x’ term, i.e. b, including its sign.

c) now factorize the product ‘ a*c ‘ (including its sign) in such a way that the multiplication of the factors gives the number ‘ a*c'(obviously) and the addition/subtraction gies the number ‘ b ‘.

d) replace ‘b’ by the addition/ subtraction form of these factors.

e) then consideing wo terms at a time, take out the common factor and proceed.

Equation 3 is worked out as an example of the procedure as shown.

Once square is completed solve it !!

Conidering the equations 1 and 2.

Unlike eqn 3, equations 1 and 2 cannot be fatorized as perfect square. To solve by completion of squares in these two cases, the following steps are followed :

a) write the eqn in descening powers of X.

b) add and subrtract the term in the given equation.

c) The first three terms thus form a quadratic equation which on factorization (by method shown above) gives perfect square, and the latter terms are simplified to a whole number.

d) thus square is completed and then solved.

Eqn 1 and 2 are solved as example.