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 numbers. Then, solve the equation. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. Form: Solution: \( (x-\square)^{2} \)

Solve the equation \( x^{2}-14x+35=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}-14x+35=0\) - step1: Solve using the quadratic formula: \(x=\frac{14\pm \sqrt{\left(-14\right)^{2}-4\times 35}}{2}\) - step2: Simplify the expression: \(x=\frac{14\pm \sqrt{56}}{2}\) - step3: Simplify the expression: \(x=\frac{14\pm 2\sqrt{14}}{2}\) - step4: Separate into possible cases: \(\begin{align}&x=\frac{14+2\sqrt{14}}{2}\\&x=\frac{14-2\sqrt{14}}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&x=7+\sqrt{14}\\&x=\frac{14-2\sqrt{14}}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=7+\sqrt{14}\\&x=7-\sqrt{14}\end{align}\) - step7: Rewrite: \(x_{1}=7-\sqrt{14},x_{2}=7+\sqrt{14}\) The solutions to the quadratic equation \(x^{2}-14x+35=0\) by completing the square are \(x_{1}=7-\sqrt{14}\) and \(x_{2}=7+\sqrt{14}\).