Answer:
x = (-1/4)(1 ± √33)
Step-by-step explanation:
Let's "complete the square."
This procedure requires taking half of the coefficient of x and squaring it:
Half of 1/2 is 1/4, and the square of 1/4 is 1/16.
Then we have:
x^2 + (1/2)x + 1/16 = 2 + 1/16 = 33/16
Rewriting x^2 + (1/2)x + 1/16 as the square of a binomial, we get:
(x + 1/4)^2 = 33/16
We must solve this for x.
Taking the sqrt of both sides, we get:
x + 1/4 = ±√33/4, or:
x = -1/4 ±√33/4, or
x = (-1/4)(1 ± √33)
