To solve the equation \( x^2 - 5x = -4 \), we first rearrange it into standard form:
\[ x^2 - 5x + 4 = 0 \]
Next, we can factor the quadratic equation. We need to find two numbers that multiply to \( 4 \) (the constant term) and add up to \( -5 \) (the coefficient of \( x \)).
The numbers that satisfy these conditions are \( -4 \) and \( -1 \). Therefore, we can factor the quadratic as follows:
\[ (x - 4)(x - 1) = 0 \]
Now, we can set each factor equal to zero to find the solutions:
\[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \] \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]
Thus, the solutions to the equation \( x^2 - 5x = -4 \) are:
\[ x = 1, \quad x = 4 \]
In order from smaller to larger, we have:
\[ x = 1, \quad x = 4 \]