solve the quadratic equation: $x^{2}-2x - 8 = 0$

Explanation:

Step1: Factor the quadratic equation

For the quadratic equation (x^{2}-2x - 8=0), we need to find two numbers (a) and (b) such that (a + b=-2) and (a\times b=-8). The numbers are (a = 2) and (b=-4). So, (x^{2}-2x - 8=(x - 4)(x + 2)=0)

Step2: Use the zero - product property

If ((x - 4)(x + 2)=0), then either (x-4 = 0) or (x + 2=0)

When (x-4=0), we get (x = 4)

When (x + 2=0), we get (x=-2)

Answer:

(x = 4) or (x=-2)