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
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
Similarly, following the same procedure, we can solve other Quadratic Equations.