what is the solution to the equation $sqrt{-5p}=sqrt{24 - p}$?\n$p=-6$\n$p =-\frac{24}{5}$\n$p=-4$\n$p=-\frac…

Explanation:

Step1: Square both sides

Since $\sqrt{-5p}=\sqrt{24 - p}$, squaring both sides gives $-5p=24 - p$.

Step2: Isolate the variable

Add $5p$ to both sides: $0 = 24 - p+5p$, which simplifies to $0 = 24 + 4p$. Then subtract 24 from both sides: $-24=4p$.

Step3: Solve for $p$

Divide both sides by 4: $p=\frac{-24}{4}=-6$.

Step4: Check the solution

For the original equation $\sqrt{-5p}=\sqrt{24 - p}$, when $p = - 6$, the left - hand side is $\sqrt{-5\times(-6)}=\sqrt{30}$, and the right - hand side is $\sqrt{24-(-6)}=\sqrt{30}$. The solution is valid.

Answer:

$p=-6$