solve x^2 = 5x + 2 by completing the square

[dkarolasz]

Could someone let me know if i did this right.

solve by completing the square

x^2=5x+2

to complete the square the middle term must be of the 2 x a x b so we get

x2 - 2 x( 5/2 x X) + ( 5/2)2+ 2 - (5/2)2 =( x -5/2)2 +2-25/4 or we get ( x-5/2 )2=17/4 so we get


x = 5/2 + or - root 17/2 so the solutions are x = 5/2+ or - (square root 17) /2

 

[Denis]

Noooooo; in order to see where you're at:
can you solve x^2 - 5x - 2 = 0 using the quadratic formula?

 

[morson]

For $\displaystyle x^2 + bx + c$

This is equal to: $\displaystyle x^2 + bx + (\frac{b}{2}$^2 - (\frac{b}{2}\)^2 + c\)

You see how the expression $\displaystyle (\frac{b}{2}$^2\) has been added and subtracted, which doesn't change the expression at all. Notice also that the first three terms form the expansion of $\displaystyle (x + \frac{b}{2}$^2\), so the expression becomes:

$\displaystyle (x + \frac{b}{2}$^2 + c - (\frac{b}{2}\)^2\)