Answer:
x = - 8 is an extraneous solution
Step-by-step explanation:
Given
[tex]\sqrt{4x+41}[/tex] = x + 5 ( to clear the radical, square both sides )
4x + 41 = (x + 5)² ← expand using FOIL
4x + 41 = x² + 10x + 25 ( subtract 4x + 41 from both sides )
0 = x² + 6x - 16 ← in standard form
0 = (x + 8)(x - 2) ← in factored form
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 2 = 0 ⇒ x = 2
As a check
Substitute these values into the equation and if both sides are equal then they are solutions.
x = - 8
left side = [tex]\sqrt{-32+41}[/tex] = [tex]\sqrt{9}[/tex] = 3
right side = - 8 + 5 = - 3 ≠ 3 → Thus not a solution
x = 2
left side = [tex]\sqrt{8+41}[/tex] = [tex]\sqrt{49}[/tex] = 7
right side = 2 + 5 = 7 → thus a solution
x = 2 is a solution and x = - 8 is an extraneous solution
