Solve the following equation by factorization:

$\sqrt{x + 15}$ = (x + 3)

Given,

⇒ $\sqrt{x + 15}$ = (x + 3)

Squaring both sides, we get :

⇒ (x + 15) = (x + 3)²

⇒ x + 15 = (x)² + (3)² + 2 × x × 3

⇒ x + 15 = x² + 9 + 6x

⇒ x² + 9 + 6x - x - 15 = 0

⇒ x² + 5x - 6 = 0

⇒ x² + 6x - x - 6 = 0

⇒ x(x + 6) - 1(x + 6) = 0

⇒ (x + 6)(x - 1) = 0

⇒ (x + 6) = 0 or (x - 1) = 0      [Using Zero-product rule]

⇒ x = -6 or x = 1.

Substituting x = -6 in the L.H.S. of this equation $\sqrt{x + 15}$ = (x + 3)

$\Rightarrow \sqrt{-6 + 15} \\[1em] \Rightarrow \sqrt{9} \\[1em] \Rightarrow 3$

Substituting x = -6 in the R.H.S. of this equation $\sqrt{x + 15}$ = (x + 3)

⇒ x + 3

⇒ -6 + 3

⇒ -3.

L.H.S ≠ R.H.S .

∴ x = -6 is not valid.

Hence, x = {1}.