Expert: Sherman D. - 1/23/2005

Question
Hello, I'm Nate, a 14-year old freshman at Exeter Academy. I feel too embarrassed to ask my peers this question because I'm sure they have it covered in-depth, but  how do you do the following, or why, for that matter.

"In solving an equation such as 2x^2-5x=3 by completing the square, it is customary to first divide each term by two so that the coefficient of x is 1. This transforms the equation into x^2-5/2x = 3/2. Now continue to solve by the completing the square method, remembering to take half of 5/2, square it and add it to both sides of the equation. Complete the solution."

Answer
2x^2 - 5x = 3
x^2 - (5/2)x = (3/2)

find half of (5/2), then square it, and add it to both sides

x^2 - (5/2)x + (25/16) = (49/16)

factor left side into a perfect square

(x - (5/4))^2 = (49/16)

sqrt both sides

x - (5/4) = ±(7/4)

add (5/4) from both sides

x = (5/4) ± (7/4)
x = (5 + 7)/4 or (5 - 7)/4
x = (12/4) or (-2/4)
x = 3 or (-1/2)