How do you solve x^2 - 6x + 6 = 0x26x+6=0?

1 Answer
Aug 2, 2015

The solutions are:
color(blue)(x=3+sqrt(3)x=3+3
color(blue)(x=3-sqrt(3)x=33

Explanation:

x^2-6x+6x26x+6

The equation is of the form color(blue)(ax^2+bx+c=0ax2+bx+c=0 where:
a=1, b=-6, c=6a=1,b=6,c=6

The Discriminant is given by:
Delta=b^2-4*a*c
= (-6)^2-(4*(1)*6)
= 36-24 = 12

As Delta>0 there are two solutions.

The solutions are found using the formula:
x=(-b+-sqrtDelta)/(2*a)

x = (-(-6)+-sqrt(12))/(2*1) = (6+-sqrt(12))/2

sqrt12=sqrt(2*2*3) = 2sqrt3

x=(6+-2sqrt(3))/2
x=(cancel2(3+-sqrt(3)))/cancel2
x=3+-sqrt(3)

The solutions are:
color(blue)(x=3+sqrt(3)
color(blue)(x=3-sqrt(3)