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Make a coordinate grid and plot the point (1,2).
Now draw a vertical line from (1,2) down to (1,0). That segment is of length 2 (the distance between (1,2) and (1,0)) and is one leg of a right triangle.
We want to find a point on the x axis that will include the drawn segment and result in a right triangle with hypotenuse of length
There are two points that are solutions. One point is to the left of (1,0) and the other is an equal distance to the right of (1,0).
So how far is that distance?
Use the Pythagorean theorem.
You know the length of two sides of a right triangle, so you can solve for the third side.
So the points are 3 units on either side of (1,0). That means (4,0) and (-2,0)
are the two points that are solutions.