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

Question

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

Answer 1

(x -2)2 = -8

Dividing both sides by 2

then (X-2) = -4

Adding 2 to both sides we obtain

X=-2

Answer 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.

 

 

Answer 3

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.