Rewrite the equation by completing the square. \( 2 x^{2}-11 x+14=0 \) \( (x+\square)^{2}=\square \)

To complete the square for the equation \( 2 x^{2}-11 x+14=0 \), first, divide everything by 2: \[ x^{2} - \frac{11}{2} x + 7 = 0 \] Next, move the constant to the other side: \[ x^{2} - \frac{11}{2} x = -7 \] Now, take half of the coefficient of \( x \) (which is \(-\frac{11}{2}\)), square it, and add it to both sides. Half of \(-\frac{11}{2}\) is \(-\frac{11}{4}\), and squaring it gives \(\left(-\frac{11}{4}\right)^2 = \frac{121}{16}\). Add this to both sides: \[ x^{2} - \frac{11}{2} x + \frac{121}{16} = -7 + \frac{121}{16} \] Convert \(-7\) into sixteenths: \[ -7 = -\frac{112}{16} \] So our equation now looks like this: \[ x^{2} - \frac{11}{2} x + \frac{121}{16} = \frac{121}{16} - \frac{112}{16} = \frac{9}{16} \] The left side can be factored: \[ \left(x - \frac{11}{4}\right)^{2} = \frac{9}{16} \] Thus, the completed square form is: \[ \left(x - \frac{11}{4}\right)^{2} = \frac{9}{16} \] So, in your desired format: \((x - \frac{11}{4})^{2}=\frac{9}{16}\)