X2+4x-5=0

To solve the quadratic equation \( x^2 + 4x - 5 = 0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this equation, \( a = 1 \), \( b = 4 \), and \( c = -5 \). Now, we can substitute these values into the formula: 1. Calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = 4^2 - 4 \cdot 1 \cdot (-5) = 16 + 20 = 36 \] 2. Now apply the quadratic formula: \[ x = \frac{-4 \pm \sqrt{36}}{2 \cdot 1} = \frac{-4 \pm 6}{2} \] This gives us two possible solutions: \[ x_1 = \frac{-4 + 6}{2} = \frac{2}{2} = 1 \] \[ x_2 = \frac{-4 - 6}{2} = \frac{-10}{2} = -5 \] Thus, the solutions to the equation \( x^2 + 4x - 5 = 0 \) are: \[ x = 1 \quad \text{and} \quad x = -5 \]