Respuesta :
Answer:
see explanation
Step-by-step explanation:
given
x + 4 = [tex]\sqrt{x+10}[/tex] ( square both sides )
(x + 4)² = x + 10
x² + 8x + 16 = x + 10
rearrange into standard form : ax² + bx + c = 0
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 these values into the equation and if the left side equals the right side then they are solutions
x = - 1 : left = - 1 + 4 = 3 , right = [tex]\sqrt{-1+10}[/tex] = [tex]\sqrt{9}[/tex] = 3
Hence x = - 1 is a solution
x = - 6 : left = - 6 + 4 = - 2 , right = [tex]\sqrt{-6+10}[/tex] = [tex]\sqrt{4}[/tex] = 2
Hence x = - 6 is an extraneous solution
Answer:
C The solution -6 is extraneous
Step-by-step explanation:
got it right on edge
