By completing the square, x² + 6x + 5 = 0 becomes (x + 3)² = k. Find k.

4. x² + 6x + 5 = (x + 3)² − 9 + 5 = (x + 3)² − 4. Setting equal to 0 gives (x + 3)² = 4, so k = 4.

By completing the square, $x^{2} + 6 x + 5 = 0$ becomes $(x + 3)^{2} = k$ . Find $k$ .

Class 10Quadratic EquationsAlgebra — Quadratics

x^{2} + 6 x + 5 = (x + 3)^{2} - 9 + 5 = (x + 3)^{2} - 4

. Setting equal to 0 gives

(x + 3)^{2} = 4

, so

k = 4

Answer: A) 4

Rewrite

a x^{2} + b x + c

into the form

a (x - h)^{2} + k

.

**Steps for

x^{2} + b x + c = 0

**:
1. Take half the coefficient of

x : b /2

.
2. Square it:

(b /2)^{2}

.
3. Add and subtract this value to complete the perfect square.

Example:

x^{2} + 6 x + 5 = 0

.
→

(x^{2} + 6 x + 9) - 9 + 5 = 0

→

(x + 3)^{2} = 4

→

x + 3 =

±2 →

x = - 1

or −5.

Completing the square is how the quadratic formula is DERIVED. It's slower than factorisation but works ALWAYS (no clever guessing required).

Don't just memorise the answer — build a daily practice habit.