We know that in any triangle the side opposite to the angle with the largest measure is always the longest side ( i.e the side with largest length) and the side opposite to the smallest angle measure is the shortest side ( i.e. the side with shortest side length ).
Hence, here we are asked what is opposite the angle with the greatest measure:
In can be less mental effort if the equation is multiplied by -1 first. .. x^2 -10x +8 = 0 .. x^2 -10x +25 +8 -25 = 0 .. (x -5)^2 = 17 .. x -5 = ±√17 .. x = 5 ±√17
The values of x that satisfy the given equation are .. x = 5 -√17 ≈ 0.877 .. x = 5 +√17 ≈ 9.123
