Solve the quadratic equation by completing the square. \[ x^{2}-14 x+35=0 \] First, choose the appropriate form and fill in the blanks with the correct num Then, solve the equation. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. \[ (4+\square)^{2}=\square \] Form: \[ \left(x-D^{2}=\square\right. \]

To solve the quadratic equation \( x^{2}-14 x+35=0 \) by completing the square, we first need to manipulate the equation to a specific form. 1. Rewrite the equation: \[ x^{2} - 14x + 35 = 0 \] Move 35 to the other side: \[ x^{2} - 14x = -35 \] 2. To complete the square, we take half of the coefficient of \( x \) (which is -14), square it, and add it to both sides. Half of -14 is -7, and squaring it gives us \( 49 \): \[ x^{2} - 14x + 49 = -35 + 49 \] This simplifies to: \[ x^{2} - 14x + 49 = 14 \] 3. Now, we can write the left side as a squared term: \[ (x - 7)^{2} = 14 \] Now we can fill in the blanks: \[ (4+\textcolor{red}{3})^{2}=\textcolor{red}{14} \] Form: \[ \left(x-\textcolor{red}{7}^{2}=\textcolor{red}{14}\right. \] 4. Next, take the square root of both sides: \[ x - 7 = \pm \sqrt{14} \] 5. Solve for \( x \): \[ x = 7 \pm \sqrt{14} \] The solutions are: \[ x = 7 + \sqrt{14}, 7 - \sqrt{14} \] So the final answers, simplified, are: \[ 7 + \sqrt{14}, 7 - \sqrt{14} \]