x = - 1
given [tex]\sqrt{(1-3x)}[/tex] = 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 : [tex]\sqrt{1+3 }[/tex] = 2 and - 1 + 3 = 2 ← true
x = - 8 : [tex]\sqrt{1+24}[/tex] = 5 and - 8 + 3 = -5 ← false
thus the only solution is x = - 1
