**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**.