**Solving A Quadratic Equation By Completing The Square**

Every quadratic equation can be converted in the form:

(x + a)^{2} – b^{2} = 0 or (x – a)^{2} – b^{2} = 0.

**Steps:**

1. Bring, if required, all the term of the quadratic equation to the left hand side.

2. Express the terms containing x as x^{2} + 2xy or x^{2} – 2xy.

3. Add and subtract y2 to get x^{2} + 2xy + y^{2} – y^{2} or x^{2} – 2xy + y^{2} – y^{2}; which gives

(x + y)^{2} – y^{2} or (x – y)^{2} – y^{2}.

Thus,

(i) x^{2} + 8x = 0 ⇒ x^{2} + 2x × 4 = 0

⇒ x^{2} + 2x × 4 + 4^{2} – 4^{2} = 0

⇒ (x + 4)^{2} – 16 = 0

(ii) x^{2} – 8x = 0 ⇒ x^{2} – 2 × x × 4 = 0

⇒ x^{2} – 2 × x × 4 + 4^{2} – 4^{2} = 0

⇒ (x – 4)^{2} – 16 = 0

**Solving A Quadratic Equation By Completing The Square With Examples**

**Example 1: **Find the roots of the quadratic equation 2x^{2} – 7x + 3 = 0

(if they exist) by the method of completing the square.

**Sol. ** 2x^{2} – 7x + 3 = 0

** **[Dividing each term by 2]

**Example 2: **Find the roots of the quadratic equation 4x^{2} + 4√3x + 3 = 0

**Sol. ** 4x^{2} + 4√3x + 3 = 0

**Example 3: ** Find the roots of the quadratic equation 2x^{2} + x + 4 = 0

**Sol. **2x^{2} + x + 4 = 0

This is not possible as the square of a real number can not be negative.

**Foe More Solved Examples**

Julie says

This helps a lot of marks which I had gain .

Neha says

U r right. .

rajveer yadav says

very nice but in video very nice

Aanchal says

Nice…….it help aa lot for studies

Rakesh anupam solanki says

This is very helpful for all of us ….and we must tell about this website to all of our classmates.