# Argh

• Oct 6th 2005, 04:30 AM
x-disturbed-x
Argh
Every week I always have to spend hours trying to understand what we did in the lesson, here's the latest thing that's making me feel worthless.

Solve the Quadratic Equation by completing the square leaving the answer in surd form

10 = 3x - x^2

rearranged i know it's

x^2 - 3 = 10 (i think)

Please help! (This is the hardest one, so if I can do this the others shouldn't present a problem)
• Oct 6th 2005, 08:18 AM
TheBrain
When you are asked to complete a sqaure you must end up with something like " (X + something)² + something else = 0 "

If for example you have (X + A)² this gives X²+ 2A.X + A²
You should be able to multiply out brackets ;)

The point of completing the square is to do that in reverse.
With your equation you have:
X² - 3X + 10 = 0

With my example you will notice that I had 'A' inside the bracket, and 2A as the coefficent for X. Conversely you have -3X, so inside the bracket you need -1.5.

(X-1.5)²

However this is not the correct answer. If you were to multiply out that bracket you would end up with a + 2.25 (-1.5x-1.5), instead of the +10 that you want. The solution to this is just put another +7.75 on the end of that.

Hence after completing the square:

X² - 3X + 10 = 0 is the same as (X - 1.5)² + 7.75 = 0

I believe this is correct. :)

edit : Not quite sure what it means by surd form. I thought that was to do with square roots....