Answer: Option B
[tex]x_1 = 2[/tex] and [tex]x_2 = 8[/tex]
Step-by-step explanation:
We have the equation [tex]x ^ 2 -10x +16 = 0[/tex] and we want to solve for x.
To solve we can factor the expression and write it as the product of 2 factors.
To do this we must look for 2 numbers h and k such that adding h + k results in -10, and multiplying h*k results in 16.
Then the expression will have the form:
[tex]x ^ 2 -10x +16 = (x+h)(x+k) = 0[/tex]
You can verify that these numbers are:
[tex]h = -8\\k = -2[/tex]
Then we have to:
[tex]x ^ 2 -10x +16 = (x-8)(x-2) = 0[/tex]
Then the solutions are:
[tex]x_1 = 2[/tex] and [tex]x_2 = 8[/tex]
