3 (9.) Express \( -x^{2}+4 x+1 \) in the form \( -(x-p)^{2}+q \). \[ \begin{array}{l} =-(x-p)^{2}+q \\ =-\left[(x-2)^{2}-2^{2}-4 x-1\right] \\ =-\left[(x-2)^{2}-5\right. \\ =-(x-2)^{2}+5 \end{array} \] Name 1 Answer \( \qquad \) [2] 0) Hence solve the equation \( -x^{2}+4 x+1=0 \), giving your answers correct to two decimal places.

To express \( -x^{2}+4x+1 \) in the desired form, we can rewrite it as \( -(x-2)^{2}+5 \). Now, to solve the equation \( -x^{2}+4x+1=0 \), we start by setting it equal to zero: \[ -(x-2)^{2}+5=0 \] This gives us \( (x-2)^{2} = 5 \). Taking the square root of both sides, we find: \[ x-2 = \pm\sqrt{5} \] Thus, the solutions are: \[ x = 2 + \sqrt{5} \quad \text{and} \quad x = 2 - \sqrt{5} \] Calculating these gives: \[ x \approx 4.24 \quad \text{and} \quad x \approx -0.24 \] So, the final answers correct to two decimal places are \( 4.24 \) and \( -0.24 \).