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(x -2)2 if the value = -8

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

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Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
5.0 5.0 (1 lesson ratings) (1)
(x -2)2 = -8
Dividing both sides by 2
then (X-2) = -4
Adding 2 to both sides we obtain
Kevin C. | Successful Math Tutor -- Recently retired high school math teacherSuccessful Math Tutor -- Recently retire...
5.0 5.0 (556 lesson ratings) (556)
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.
Suneil P. | Knowledgeable and Passionate University of Pennsylvania Math TutorKnowledgeable and Passionate University ...
5.0 5.0 (25 lesson ratings) (25)
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: x2-4x+4=-8 ---> x2-4x+12=0.  Using the quadratic formula, we get x=2±2i√2, exactly as obtained before.
Hope this helps.


If this was not the way in which it was meant to be written, please feel free to ignore this :)
All are excellent answers as long as the problems that we are solved are the true one. We are here not to guess but to solve what is in front of our eyes. Probably the answer of Kevin is the one to be picked or the one given by Suneil but are we solving the need of the student?