X2 +11x-12=0

To solve the quadratic equation \( x^2 + 11x - 12 = 0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this equation, \( a = 1 \), \( b = 11 \), and \( c = -12 \). First, we calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = 11^2 - 4(1)(-12) = 121 + 48 = 169 \] Now, we can use this in the quadratic formula: \[ x = \frac{-11 \pm \sqrt{169}}{2(1)} \] Calculating \( \sqrt{169} \): \[ \sqrt{169} = 13 \] Now, substituting back into the formula gives: \[ x = \frac{-11 \pm 13}{2} \] This leads to two possible solutions for \( x \): 1. \( x = \frac{-11 + 13}{2} = \frac{2}{2} = 1 \) 2. \( x = \frac{-11 - 13}{2} = \frac{-24}{2} = -12 \) Therefore, the solutions to the equation \( x^2 + 11x - 12 = 0 \) are: \[ x = 1 \quad \text{and} \quad x = -12 \]