Question

What is the solution of sqrt1-3x=x+3

Answer 1

x = - 1

given $\sqrt{(1-3x)}$ = x + 3

square both sides

1 - 3x = (x + 3 )² ( expand right side using FOIL )

1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )

0 = x² + 9x + 8

0 = ( x + 1)(x + 8)

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = -1

x + 8 = 0 ⇒ x = - 8

As a check

substitute these values into the equation and if both sides are equal then they are the solutions

x = - 1 : $\sqrt{1+3 }$ = 2 and - 1 + 3 = 2 ← true

x = - 8 : $\sqrt{1+24}$ = 5 and - 8 + 3 = -5 ← false

thus the only solution is x = - 1