To solve the equation \( x^2 - 5x = -4 \), we first rearrange it into standard form:
\[ x^2 - 5x + 4 = 0 \]
Now, we can factor the quadratic equation:
\[ (x - 1)(x - 4) = 0 \]
Setting each factor equal to zero gives us the solutions:
\[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]
\[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \]
So the solutions to the equation are \( x = 1 \) and \( x = 4 \).
Putting the smaller value first, we have:
\[ x = 1, \quad x = 4 \]
Thus, the solutions are:
- \( x = 1 \)
- \( x = 4 \)
If you're interested in graphing the function to visualize these solutions, you'd graph \( y = x^2 - 5x + 4 \) and observe where it intersects the x-axis (i.e., where \( y = 0 \)). The points of intersection will correspond to the solutions we found: \( (1, 0) \) and \( (4, 0) \).
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