x(x-5)=-4

To solve the equation \( x(x - 5) = -4 \), we can start by rearranging it into standard quadratic form.

1. Expand the left side: \[ x^2 - 5x = -4 \]

2. Move all terms to one side of the equation to set it to zero: \[ x^2 - 5x + 4 = 0 \]

Now we have a quadratic equation in the form \( ax^2 + bx + c = 0 \) where \( a = 1 \), \( b = -5 \), and \( c = 4 \).

Next, we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Plugging in the values: \[ x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 4}}{2 \cdot 1} \] \[ x = \frac{5 \pm \sqrt{25 - 16}}{2} \] \[ x = \frac{5 \pm \sqrt{9}}{2} \] \[ x = \frac{5 \pm 3}{2} \]

This gives us two possible solutions:

1. \( x = \frac{5 + 3}{2} = \frac{8}{2} = 4 \)
2. \( x = \frac{5 - 3}{2} = \frac{2}{2} = 1 \)

Thus, the solutions to the equation \( x(x - 5) = -4 \) are: \[ x = 4 \quad \text{and} \quad x = 1 \]