Questions: Solve the following equation by factoring. x^2-8x=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is 3. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

Solve the following equation by factoring. x^2-8x=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is 3. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.
Transcript text: Solve the following equation by factoring. \[ x^{2}-8 x=0 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ 3. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.
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Solution

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Solution Steps

Step 1: Rewrite the equation

The given equation is: \[ x^{2} - 8x = 0 \]

Step 2: Factor the equation

Factor out the common term \( x \): \[ x(x - 8) = 0 \]

Step 3: Solve for \( x \)

Set each factor equal to zero and solve: \[ x = 0 \quad \text{or} \quad x - 8 = 0 \] \[ x = 0 \quad \text{or} \quad x = 8 \]

Step 4: Write the solution set

The solution set is: \[ \{0, 8\} \]

Final Answer

The solution set is \(\boxed{0, 8}\).

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