Find the roots of the following quadratic equation: \[ -x^{2}-22 x=-48 \]

To solve the quadratic equation \(-x^2 - 22x = -48\), first, let's rearrange it into standard form. Adding \(48\) to both sides gives: \[ -x^2 - 22x + 48 = 0 \] Next, we can multiply the entire equation by \(-1\) to simplify it: \[ x^2 + 22x - 48 = 0 \] Now, we can use the quadratic formula, where \(a = 1\), \(b = 22\), and \(c = -48\): \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \] Calculating the discriminant: \[ b^2 - 4ac = 22^2 - 4(1)(-48) = 484 + 192 = 676 \] Now, plug the values into the formula: \[ x = \frac{{-22 \pm \sqrt{676}}}{2(1)} = \frac{{-22 \pm 26}}{2} \] Calculating the two potential roots: 1. \(x = \frac{{-22 + 26}}{2} = \frac{4}{2} = 2\) 2. \(x = \frac{{-22 - 26}}{2} = \frac{-48}{2} = -24\) Thus, the roots of the equation are: \[ x = 2 \quad \text{and} \quad x = -24 \]