Question 134721
You've done great work ... and almost all the hard part too.

In order to be a root, the value of 
{{{(x^2-4x+53)(x^2-2x+10)}}} must be 0 at that point
In order for a product to be 0, one or both terms must be zero.

So set {{{(x^2-2x+10)=0}}} and solve using the quadratic equation
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

You don't need to solve the term {{{x^2-4x+53)}}} since you generated that from the two given root.

Nice work!