a) \( x(x-2)=35 \)

To solve the equation \( x(x-2)=35 \), first, we rearrange it to form a standard quadratic equation: \( x^2 - 2x - 35 = 0 \). You can use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -2 \), and \( c = -35 \). Plugging those values in gives you the solutions for \( x \). Once you find the roots, you can verify them by substituting back into the original equation to confirm they're correct. Remember, double-checking your steps helps avoid simple arithmetic errors.