Find X using the given information

Just so you hear, Whirlybot,  these circle problems are always "tricks"  and they are tough.  You have to remember a bunch of implied things

Step-by-step explanation:

One thing to recall is that the angle from the tangent point to O at the center is also a 90° angle.  so you now know, that the line from the point where the circle touches the tangent line to the center is a right angle and you have part of that 90° already.  the 50 is one part and there for the next part is 40 °  Since we now know that the line from the tangent to the center is forming an internal angle with that line going to X of 40 °  we know that X is also 40 ° b/c the triangle formed by the line to the center is going to be the same length as the line from the center to the X.  That's an Isosceles triangle.  they have the same angles at the two same length legs.  

I know, I went thur a whole pile of logic, but that's what makes this kind of problem tough.   you just have to keep thinking about things you know.

X = 40 °

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81