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To solve the equation x^2 - 4x - 8 = 0, we can use the quadratic formula:
x = (-(-4) ยฑ sqrt((-4)^2 - 4(1)(-8))) / 2(1)
x = (4 ยฑ sqrt(16 + 32)) / 2
x = (4 ยฑ sqrt(48)) / 2
x = (4 ยฑ 4โ3) / 2
Therefore, the two solutions are:
x = (4 + 4โ3) / 2 = 2 + 2โ3
or
x = (4 - 4โ3) / 2 = 2 - 2โ3
So, the solutions to the equation x^2 - 4x - 8 = 0 are x = 2 + 2โ3 and x = 2 - 2โ3.