Question

x squared minus 4 x minus 6 equals 0

Answer 1

To solve the equation \( x^2 - 4x - 6 = 0 \), we can use the quadratic formula:

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

where \( a = 1 \), \( b = -4 \), and \( c = -6 \).

First, we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = (-4)^2 - 4 \cdot 1 \cdot (-6) = 16 + 24 = 40
\]

Now we can plug the values into the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{40}}{2 \cdot 1} = \frac{4 \pm \sqrt{40}}{2}
\]

The square root of 40 can be simplified:

\[
\sqrt{40} = \sqrt{4 \cdot 10} = 2\sqrt{10}
\]

So, our equation becomes:

\[
x = \frac{4 \pm 2\sqrt{10}}{2}
\]

Now, we simplify further:

\[
x = 2 \pm \sqrt{10}
\]

Thus, the solutions to the equation \( x^2 - 4x - 6 = 0 \) are:

\[
x = 2 + \sqrt{10} \quad \text{and} \quad x = 2 - \sqrt{10}
\]