Question

x^2 + 5x - 6 = 0 quadratic formula

Answer 1

To solve the quadratic equation \( x^2 + 5x - 6 = 0 \) using the quadratic formula, we first identify the coefficients \( a \), \( b \), and \( c \) from the standard form of the quadratic equation \( ax^2 + bx + c = 0 \).

Here, we have:
- \( a = 1 \)
- \( b = 5 \)
- \( c = -6 \)

The quadratic formula is given by:

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

Now, we can substitute the values of \( a \), \( b \), and \( c \) into the formula:

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

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

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

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

3. Calculate the two possible values for \( x \):

- For the positive root:

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

- For the negative root:

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

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

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