Question

Solve the following equation by factorization:

`sqrt(2x + 9) = (13 - x)`

Solve for x: 

`sqrt(2x + 9) + x = 13`

Answer 1

Given,

⇒ `sqrt(2x + 9) = (13 - x)`

Or Given, 

⇒ `sqrt(2x + 9) + x = 13`

⇒ `sqrt(2x + 9) = 13 - x`

Squaring both sides we get:

⇒ (2x + 9) = (13 – x)² 

⇒ 2x + 9 = (13²) + (x)² – 2 × 13 × x

⇒ 2x + 9 = 169 + x² – 26x

⇒ x² – 26x + 169 – 2x – 9 = 0

⇒ x² – 28x + 160 = 0

⇒ x² – 20x – 8x + 160 = 0

⇒ x(x – 20) – 8(x – 20) = 0

⇒ (x – 20)(x – 8) = 0

⇒ (x – 20) = 0 or (x – 8) = 0   ...[Using zero-product rule]

⇒ x = 20 or x = 8

⇒ x = 8

Substituting x = 20 in the L.H.S. of this equation `sqrt(2x + 9) = (13 - x)`

⇒ `sqrt(2(20) + 9)`

⇒ `sqrt(40 + 9)`

⇒ `sqrt(49)`

⇒ 7

Substituting x = 20 in the R.H.S. of this equation `sqrt(2x + 9) = (13 - x)`

⇒ 13 – x

⇒ 13 – 20

⇒ –7

L.H.S ≠ R.H.S.

∴ x = 20 is not valid.

Hence, x = {8}.