Which of the following is a solution to the equation `x^(2) - 36x = 0` ?

Options

A. 72
B. 36
C. 18
D. 6

Answer

To solve the equation \( x^2 - 36x = 0 \), we will follow these steps:

### Step 1: Write down the equation
We start with the equation:
\[ x^2 - 36x = 0 \]

### Step 2: Factor the equation
Next, we factor out the common term \( x \) from the left-hand side:
\[ x(x - 36) = 0 \]

### Step 3: Set each factor to zero
Now, we set each factor equal to zero:
1. \( x = 0 \)
2. \( x - 36 = 0 \)

### Step 4: Solve for \( x \)
From the second equation, we solve for \( x \):
\[ x - 36 = 0 \implies x = 36 \]

### Step 5: List the solutions
The solutions to the equation are:
1. \( x = 0 \)
2. \( x = 36 \)

### Step 6: Identify the valid solution
Since the question asks for a solution among the options provided (72, 36, 18, 6), we check which of these is a solution. The valid solution from our calculations is:
\[ x = 36 \]

### Conclusion
Thus, the correct answer is option B: 36.

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