X2-2x-4=0
To solve the quadratic equation \( x^2 - 2x - 4 = 0 \), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, the coefficients are:
- \( a = 1 \)
- \( b = -2 \)
- \( c = -4 \)
Now, we can substitute these values into the quadratic formula:
Calculate the discriminant (\( b^2 - 4ac \)): \[ (-2)^2 - 4 \cdot 1 \cdot (-4) = 4 + 16 = 20 \]
Substitute the values into the quadratic formula: \[ x = \frac{-(-2) \pm \sqrt{20}}{2 \cdot 1} \] \[ x = \frac{2 \pm \sqrt{20}}{2} \]
Simplify \( \sqrt{20} \): \[ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} \]
Now substitute back: \[ x = \frac{2 \pm 2\sqrt{5}}{2} \] \[ x = 1 \pm \sqrt{5} \]
Thus, the solutions to the equation \( x^2 - 2x - 4 = 0 \) are: \[ x = 1 + \sqrt{5} \quad \text{and} \quad x = 1 - \sqrt{5} \]
