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To solve this problem, we need to find the value of \( m \) such that the curve of the function \( f(x) = x^2 + 10x + (m - 1) \) is tangent to the x-axis.

For a quadratic function \( ax^2 + bx + c \), the condition for the curve to be tangent to the x-axis is that the discriminant \( \Delta \) equals zero. The discriminant is given by:

\[
\Delta = b^2 - 4ac
\]

In this case:
- \( a = 1 \) (coefficient of \( x^2 \)),
- \( b = 10 \) (coefficient of \( x \)),
- \( c = m - 1 \).

So, we set up the discriminant as follows:

\[
\Delta = 10^2 - 4 \cdot 1 \cdot (m - 1)
\]
\[
0 = 100 - 4(m - 1)
\]

Solving for \( m \):

\[
0 = 100 - 4m + 4
\]
\[
0 = 104 - 4m
\]
\[
4m = 104
\]
\[
m = 26
\]

Thus, the possible value of \( m \) for the curve to be tangent to the x-axis is \( m = 26 \).

Would you like further explanation or details about any part of this solution?

Here are 5 related questions for further practice:
1. What happens if the discriminant \( \Delta > 0 \) in a quadratic function?
2. How many intersection points does a parabola have with the x-axis if \( \Delta < 0 \)?
3. For the function \( f(x) = ax^2 + bx + c \), how do you determine the vertex?
4. How does the value of \( a \) in \( ax^2 + bx + c \) affect the direction of the parabola's opening?
5. If a parabola is tangent to the x-axis at \( x = p \), how can you find the value of \( p \)?

**Tip:** When solving quadratic equations, always check the discriminant to understand the nature of the roots (real and distinct, real and equal, or complex).

Agar kurva fungsi f(x) = x^2 + 10x + (m - 1) menyinggung sumbu x, maka nilai m yang mungkin adalah . . .

Learn how to determine the value of m such that the curve of the quadratic function f(x) = x^2 + 10x + (m - 1) touches the x-axis. This problem covers key algebraic concepts, including the discriminant formula and its application in finding the points of tangency.

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