Answer:
x = 16
Step-by-step explanation:
0=x^2-14x+46 is to be solved for x by completing the square. The first two terms, x^2 and -14x, are the incomplete square. We must find a term to add to, and then subtract from x^2 - 14x, so that we have a perfects square on the left and a negative number on the right:
x^2 - 14x = x^2 - 14x + (half of -14)^2 - (half of -14)^2 results in transformation of the original 0=x^2-14x+46 to
x^2 - 14x + 49 - 49 + 46 = 0, which simplifies to:
(x - 7)^2 - 3 = 0. We want to solve this for x.
To do that, rewrite (x - 7)^2 - 3 = 0 as (x - 7)^2 = 3, and then square both sides. We get:
x - 7 = 9, or x = 16
