X²-3x-28=0

To solve the quadratic equation \(x^2 - 3x - 28 = 0\), we can use the quadratic formula, which is: \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \] For the given equation, the coefficients are: - \(a = 1\) - \(b = -3\) - \(c = -28\) Now, we can substitute these values into the formula: 1. Calculate the discriminant (\(b^2 - 4ac\)): \[ b^2 - 4ac = (-3)^2 - 4(1)(-28) = 9 + 112 = 121 \] 2. Now apply the quadratic formula: \[ x = \frac{{-(-3) \pm \sqrt{121}}}{2(1)} = \frac{{3 \pm 11}}{2} \] 3. This gives us two possible solutions: \[ x_1 = \frac{{3 + 11}}{2} = \frac{14}{2} = 7 \] \[ x_2 = \frac{{3 - 11}}{2} = \frac{-8}{2} = -4 \] Thus, the solutions to the equation \(x^2 - 3x - 28 = 0\) are: \[ x = 7 \quad \text{and} \quad x = -4 \]