how to solve by factoring if (x -2)2 has the value of negative 8

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(x -2)2 = -8

Dividing both sides by 2

then (X-2) = -4

Adding 2 to both sides we obtain

X=-2

If the problem is (x-2)^{2} = -8, then |x-2| = 2i√2, and x-2 = 2i√2 and x-2 = -2i√2.

So the answers are x = 2+2i√2, and x = 2-2i√2.

I gather that the way in which you meant to write the question was (x-2)^{2}=-8.

If so, I think the easiest way to solve this is to take the +/- square root of both sides to obtain that x-2=±2i√2.

We can then solve for x to obtain x=2±2i√2.

Alternatively, (and I do not recommend this, although it may be useful in general if the root did not have a multiplicity...for instance (x-2)(x-3)=2, in which the factors are distinct), you can expand the left hand side and re-write the equation as standard form of a parabola equated to 0, and then solve for the roots.

In this problem, that would play out as: x^{2}-4x+4=-8 ---> x^{2}-4x+12=0. Using the quadratic formula, we get x=2±2i√2, exactly as obtained before.

Hope this helps.

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