Solve the following quadratic equation by either factoring or applying the Square Root Property. \( x^{2}-2 x-63=0 \)

To solve the quadratic equation \( x^{2}-2x-63=0 \) by factoring, we need to find two numbers that multiply to \(-63\) (the constant term) and add up to \(-2\) (the coefficient of \(x\)). These two numbers are \(-9\) and \(7\). Now, we can rewrite the equation as: \[ (x - 9)(x + 7) = 0 \] Setting each factor equal to zero gives the solutions: \[ x - 9 = 0 \quad \Rightarrow \quad x = 9 \] \[ x + 7 = 0 \quad \Rightarrow \quad x = -7 \] Thus, the solutions to the equation are \(x = 9\) and \(x = -7\).