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: \( (x-\square)^{2} \)

To complete the square for the equation \(x^{2} - 14x + 35 = 0\), we first need to adjust it into a perfect square format. First, we can take the coefficient of \(x\) which is \(-14\), halve it to get \(-7\), and then square it to find \(49\). We rewrite the equation as \(x^{2} - 14x + 49 - 49 + 35 = 0\), or \(x^{2} - 14x + 49 = 14\). This allows us to write it as: \( (x - 7)^{2} = 14 \). Now, let's solve for \(x\). Taking the square root of both sides gives us: \( x - 7 = \pm \sqrt{14} \). From this, we can isolate \(x\): \( x = 7 \pm \sqrt{14} \). So, the solutions to the equation are: Solution: \( 7 + \sqrt{14}, 7 - \sqrt{14} \).