Question

Solve using the quadratic formula x2 −8x−2=0 (1 point)

Answer 1

To solve the quadratic equation \(x^2 - 8x - 2 = 0\) using the quadratic formula, we can identify the coefficients:

- \(a = 1\)
- \(b = -8\)
- \(c = -2\)

The quadratic formula is given by:

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

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

\[
b^2 - 4ac = (-8)^2 - 4 \cdot 1 \cdot (-2) = 64 + 8 = 72
\]

2. Substitute the values into the quadratic formula:

\[
x = \frac{-(-8) \pm \sqrt{72}}{2 \cdot 1}
\]

This simplifies to:

\[
x = \frac{8 \pm \sqrt{72}}{2}
\]

3. Simplify \(\sqrt{72}\):

\[
\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}
\]

4. Substitute \(\sqrt{72}\) back into the formula:

\[
x = \frac{8 \pm 6\sqrt{2}}{2}
\]

5. Simplify further:

\[
x = \frac{8}{2} \pm \frac{6\sqrt{2}}{2} = 4 \pm 3\sqrt{2}
\]

Thus, the two solutions are:

\[
x = 4 + 3\sqrt{2} \quad \text{and} \quad x = 4 - 3\sqrt{2}
\]