Question

Solve for x in the quadratic equation x^2 + 5x - 6 = 0

Answer 1

To solve the quadratic equation \( x^2 + 5x - 6 = 0 \), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this equation, \( a = 1 \), \( b = 5 \), and \( c = -6 \).

1. Calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = 5^2 - 4(1)(-6) = 25 + 24 = 49
\]

2. Substitute \( a \), \( b \), and the discriminant into the quadratic formula:

\[
x = \frac{-5 \pm \sqrt{49}}{2(1)} = \frac{-5 \pm 7}{2}
\]

3. Now, calculate the two possible values for \( x \):

- For \( x_1 \):

\[
x_1 = \frac{-5 + 7}{2} = \frac{2}{2} = 1
\]

- For \( x_2 \):

\[
x_2 = \frac{-5 - 7}{2} = \frac{-12}{2} = -6
\]

Therefore, the solutions for the equation \( x^2 + 5x - 6 = 0 \) are:

\[
x = 1 \quad \text{and} \quad x = -6
\]