X²-8x+4=0

To solve the quadratic equation \(x^2 - 8x + 4 = 0\), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In your equation, \(a = 1\), \(b = -8\), and \(c = 4\). 1. **Calculate the discriminant (\(b^2 - 4ac\))**: \[ b^2 - 4ac = (-8)^2 - 4(1)(4) = 64 - 16 = 48 \] 2. **Substitute into the quadratic formula**: \[ x = \frac{-(-8) \pm \sqrt{48}}{2(1)} \] \[ x = \frac{8 \pm \sqrt{48}}{2} \] 3. **Simplify \(\sqrt{48}\)**: \(\sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}\) 4. **Continue simplifying**: \[ x = \frac{8 \pm 4\sqrt{3}}{2} \] \[ x = 4 \pm 2\sqrt{3} \] So, the solutions to the equation \(x^2 - 8x + 4 = 0\) are: \[ x = 4 + 2\sqrt{3} \quad \text{and} \quad x = 4 - 2\sqrt{3} \]