Question

what is the solution to the equation \\(\sqrt{-5p} = \sqrt{24 - p}\\)?\\(p = -\frac{24}{25}\\)\\(p = -4\\)\\(p = -\frac{24}{5}\\)\\(p = -6\\)

Explanation:

Step1: Square both sides

$$(\sqrt{-5p})^2 = (\sqrt{24-p})^2$$
$$-5p = 24 - p$$

Step2: Isolate variable terms

$$-5p + p = 24$$
$$-4p = 24$$

Step3: Solve for p

$$p = \frac{24}{-4}$$
$$p = -6$$

Step4: Verify the solution

Substitute $p=-6$ into original equation:
Left side: $\sqrt{-5\times(-6)}=\sqrt{30}$
Right side: $\sqrt{24-(-6)}=\sqrt{30}$
Both sides are equal, so the solution is valid.

Answer:

$p = -6$