QuestionQuestion Watch
Solve for all possible values of x . $$\sqrt{5 x+36}=x+8$$
Answer Attempt 1 out of 2 () Additional Solution $\Theta$ No Solution $x=$ $\square$ Submit Ans

Studdy Solution
Check each solution in the original equation to ensure they are valid:
For $x = -4$:
$$\sqrt{5(-4) + 36} = -4 + 8$$ $$\sqrt{-20 + 36} = 4$$ $$\sqrt{16} = 4$$ $$4 = 4$$ (Valid)
For $x = -7$:
$$\sqrt{5(-7) + 36} = -7 + 8$$ $$\sqrt{-35 + 36} = 1$$ $$\sqrt{1} = 1$$ $$1 = 1$$ (Valid)
Both solutions are valid.
The possible values of $x$ are:
$$\boxed{-4} \quad \text{and} \quad \boxed{-7}$$