How to solve the Quadratic Equations by completing square?
Standard form of quadratic equation is
. We will learn completing square process by two different cases. In case 1, we will have
and in case 2, we will have
.
Case 1: when a=1
Step 1: Divide middle term (bx) of given Quadratic Equation by 2x.
Step 2: Find square of result obtained in step 1.
Step 3: Add and subtract result obtained from step 2 from the given Quadratic equation.
Step 4: Combine terms of the equation obtained in step 3 to complete square.
Step 5: Get values of x.
If you are confused then go through example present below. 🙂
Lets suppose, we have Quadratic Equation
. To solve this quadratic equation by completing square, we just divide the middle term
by
and then add and subtract its square in the equation.
Dividing middle term
by
, we get
, squaring
, we get
, we add and subtract
from the equation
, we get
{
}
Taking Square root on both sides, we get
And
and
Case 2: when
We divide whole equation by
and then repeat the same process we applied in case 1.
Example, we have quadratic equation
We divide whole equation by 2 and we get
We apply same process of case 1 on the part
.
Dividing
by
, we get
. Squaring it, we get
. We will add this to the equation and subtract this from the equation
.
Square rooting on both sides, we get
and
and
and
Similarly, following the same procedure, we can solve other Quadratic Equations.
neha says
yupssss….its helpfulllll for me to understand several problems related to my ncert book…. thanks for providing this site..
neha says
gggood
john says
after doing this x2+4x+4+3−4=0
how did we get (x+2)2−1=0
Jashan says
x^2+4x+4+3-4=0
We know that (a+b)^2=a^2+2ab+b^2. Therefore, x^2+4x+4 is equal to (x+2)^2
Therefore, x^2+4x+4+3-4=(x+2)^2-1
I hope it helps.
bablu kumar says
its very helpful to me to teach my student easily thankx to providing this site
Lakshay says
Its very helpful to do my homework……………………..