Question

solve:
\sqrt{-2n - 4} - 8 = -4

Explanation:

Step1: Isolate the square root term

Add 8 to both sides of the equation $\sqrt{-2n - 4}-8=-4$.
We get $\sqrt{-2n - 4}=-4 + 8$, which simplifies to $\sqrt{-2n - 4}=4$.

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{-2n - 4}=4$.
Using the property $(\sqrt{a})^2=a$ (where $a\geq0$), we have $(\sqrt{-2n - 4})^2 = 4^2$, so $-2n-4 = 16$.

Step3: Solve for n

Add 4 to both sides: $-2n=16 + 4$, so $-2n=20$.
Divide both sides by -2: $n=\frac{20}{-2}=-10$.

Step4: Check the solution

Substitute $n = - 10$ into the original equation:
Left - hand side: $\sqrt{-2\times(-10)-4}-8=\sqrt{20 - 4}-8=\sqrt{16}-8 = 4-8=-4$, which is equal to the right - hand side.

Answer:

$n=-10$