solve the quadratic equation: $4x^{2}-4x - 8 = 0$

Explanation:

Step1: Simplify the equation

Divide the equation (4x^{2}-4x - 8=0) by (4). (x^{2}-x - 2=0)

Step2: Factor the quadratic equation

Find two numbers that multiply to (-2) and add up to (-1). These numbers are (-2) and (1). ((x - 2)(x+1)=0)

Step3: Solve for (x)

Set each factor equal to zero. If (x - 2=0), then (x = 2). If (x+1=0), then (x=-1).

Answer:

(x = 2) or (x=-1)