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The given equation is \( x^2 - 4x - 1 = 0 \).

To solve this quadratic equation, we can use the quadratic formula:

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

For the equation \( x^2 - 4x - 1 = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = -4 \)
- \( c = -1 \)

Substituting these values into the quadratic formula:

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

\[
x = \frac{4 \pm \sqrt{16 + 4}}{2}
\]

\[
x = \frac{4 \pm \sqrt{20}}{2}
\]

\[
x = \frac{4 \pm 2\sqrt{5}}{2}
\]

\[
x = 2 \pm \sqrt{5}
\]

Thus, the two solutions are:

\[
x = 2 + \sqrt{5}
\]
\[
x = 2 - \sqrt{5}
\]

Now, let's round these solutions to the nearest tenth:

\[
2 + \sqrt{5} \approx 2 + 2.236 = 4.236 \approx 4.2

Solve the following equation by any method. Round to nearest tenth: x^2 - 4x - 1 = 0

Learn how to solve the quadratic equation x^2 - 4x - 1 = 0 step-by-step using the quadratic formula. This guide covers core algebraic concepts and is perfect for students in Grades 8-10. The solution is rounded to the nearest tenth.

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