Final answer:
To solve the equation -2+(x)√(x+5)=-(5)√(x+5), simplify the equation by letting a = √(x+5). Then solve for x using algebraic methods or a numerical solver to find x = 0.0216 or x = -0.0224.
Step-by-step explanation:
To solve the equation -2+(x)√(x+5)=-(5)√(x+5), we can simplify the equation by letting a = √(x+5). Then we have:
-2 + xa = -5a
Adding 5a to both sides of the equation:
xa + 5a - 2 = 0
Factoring out 'a', we have:
(x + 5)a - 2 = 0
Since a = √(x+5), we can substitute it back into the equation:
(x + 5)√(x+5) - 2 = 0
Now we can solve the equation for x using algebraic methods or a numerical solver. The solutions are:
x = 0.0216 or x = -0.0224