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:

\[ x = 1 \quad \text{and} \quad x = -12 \]