Consider the quadratic equation shown below: \[ 2 x=x^{2}+11 \] Determine the coefficients \( a, b \), and \( c \) corresponding to the quadratic formula: \[ \begin{array}{l} a=1 \\ b=-2 \\ c=11 \end{array} \] Now enter those coefficients into the quadratic formula below: \[ x=\frac{-\square \pm \sqrt{(\square)^{2}-4 \cdot \square \cdot \square}}{2 \cdot \square} \]

To solve the quadratic equation \( 2x = x^2 + 11 \), we first need to rearrange it into the standard form \( ax^2 + bx + c = 0 \). 1. Rearranging the equation: \[ x^2 - 2x + 11 = 0 \] From this equation, we can identify the coefficients: - \( a = 1 \) - \( b = -2 \) - \( c = 11 \) Now, we can substitute these coefficients into the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Substituting the values of \( a \), \( b \), and \( c \): \[ x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot 11}}{2 \cdot 1} \] This simplifies to: \[ x = \frac{2 \pm \sqrt{4 - 44}}{2} \] \[ x = \frac{2 \pm \sqrt{-40}}{2} \] Since the discriminant (\( b^2 - 4ac \)) is negative, this indicates that the solutions will be complex numbers. Now, we can express the final form of the quadratic formula with the coefficients filled in: \[ x = \frac{-(-2) \pm \sqrt{(-2)^{2}-4 \cdot 1 \cdot 11}}{2 \cdot 1} \] Thus, the coefficients \( a, b, c \) are: - \( a = 1 \) - \( b = -2 \) - \( c = 11 \)