y = x² - 10x + 15 ---------------------------(1)
y = -10
substitute y =-10 in equation(1)
-10 = x² - 10x + 15
Rearrange
x² - 10x + 15 + 10 = 0
x² - 10x + 25 = 0
We can now solve using factorization method
Find two numbers such that its product gives 25 and its sum gives -10
The two numbers are -5 and -5
Replace -10x by -5x-5x
That is;
x² - 5x - 5x + 25 = 0
x(x - 5) -5(x-5) = 0
(x-5)(x-5) = 0
x-5 = 0
x=5
The coordinates are;
(5, -10)