If `(x-1)(x-3)=-1`, what is a possible value of x?

Answer

To solve the equation \((x-1)(x-3) = -1\), we will follow these steps:

### Step 1: Expand the left side of the equation
We start with the equation:
\[ (x-1)(x-3) = -1 \]
Expanding the left side:
\[ x^2 - 3x - x + 3 = -1 \]
This simplifies to:
\[ x^2 - 4x + 3 = -1 \]

### Step 2: Move all terms to one side
Next, we want to move \(-1\) to the left side of the equation:
\[ x^2 - 4x + 3 + 1 = 0 \]
This simplifies to:
\[ x^2 - 4x + 4 = 0 \]

### Step 3: Factor the quadratic equation
Now we can factor the quadratic equation:
\[ (x-2)(x-2) = 0 \]
This can also be written as:
\[ (x-2)^2 = 0 \]

### Step 4: Solve for x
To find the value of \(x\), we set the factor equal to zero:
\[ x - 2 = 0 \]
Thus, we find:
\[ x = 2 \]

### Conclusion
A possible value of \(x\) is:
\[ \boxed{2} \]

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