Questions: Solve for (f). [ f^2-21 f=0 ] Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. [ f=square ]

Solve for (f). [ f^2-21 f=0 ] Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. [ f=square ]
Transcript text: Solve for $f$. \[ f^{2}-21 f=0 \] Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \[ f=\square \]
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Solution

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Solution Steps

Step 1: Define the Equation

We start with the equation given in the problem: \[ f^{2} - 21f = 0 \]

Step 2: Factor the Equation

We can factor the equation as follows: \[ f(f - 21) = 0 \]

Step 3: Solve for \( f \)

Setting each factor equal to zero gives us the solutions:

  1. \( f = 0 \)
  2. \( f - 21 = 0 \) which simplifies to \( f = 21 \)

Final Answer

The solutions for the equation \( f^{2} - 21f = 0 \) are: \[ \boxed{f = 0, 21} \]

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