Answer:
x = - 6 is an extraneous solution
Step-by-step explanation:
Given
x + 4 = [tex]\sqrt{x+10}[/tex] ( square both sides )
(x + 4)² = x + 10 ← expand left side
x² + 8x + 16 = x + 10 ( subtract x + 10 from both sides )
x² + 7x + 6 = 0 ← in standard form
(x + 1)(x + 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 6 = 0 ⇒ x = - 6
As a check
Substitute each value into the equation and if both sides are equal then they are the solutions
x = - 1
left = - 1 + 4 = 3
right = [tex]\sqrt{-1+10}[/tex] = [tex]\sqrt{9}[/tex] = 3 ← True
x = - 6
left = - 6 + 4 = - 2
right = [tex]\sqrt{-6+10}[/tex] = [tex]\sqrt{4}[/tex] = 2 ≠ - 2
Thus x = - 1 is a solution and x = - 6 is an extraneous solution
