Question

Solve x^2+ 1/2x+ ___=2+___

Answer 1

x = (-1/4)(1 ± √33)

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)