Questions: Solve the following equation: 25 = sqrt(-k-1) + 3 Provide an answer accurate to the nearest hundredth.

Solve the following equation: 25 = sqrt(-k-1) + 3 Provide an answer accurate to the nearest hundredth.
Transcript text: Solve the following equation: \[ 25=\sqrt{-k-1}+3 \] Provide an answer accurate to the nearest hundredth.
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Solution

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Solution Steps

Step 1: Isolate the Square Root

Starting with the equation \[ 25 = \sqrt{-k - 1} + 3, \] we isolate the square root by subtracting 3 from both sides: \[ 25 - 3 = \sqrt{-k - 1} \implies 22 = \sqrt{-k - 1}. \]

Step 2: Square Both Sides

Next, we square both sides to eliminate the square root: \[ 22^2 = -k - 1 \implies 484 = -k - 1. \]

Step 3: Solve for \( k \)

Now, we solve for \( k \) by rearranging the equation: \[ -k = 484 + 1 \implies -k = 485 \implies k = -485. \]

Final Answer

The solution to the equation is \[ \boxed{k = -485}. \]

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