Question 35795
x2 - 3x + 2 = 0
a)Solve by factoring. 
list factors of 2; 2 and 1, when added together they 2+1=3
(x-2)(x+1)=0
x-2=0 x-1=0
x=2 or x=1

b)Solve by completing the square.
Show work in this space. 
subtract 2 from both sides; 
{{{x^2}}}-3x=0-2
half of 3=1.5; {{{1.5^2=2.25}}}
add 2.25 to both sides;
{{{x^2-3x+2.25=-2+2.25}}}
factor;
(x-1.5)(x-1.5)=.25
{{{(x-1.5)^2=.25}}}
take square root of each side;
{{{sqrt(x-1.5)^2}}}={{{sqrt(.25)}}}
x-1.5=.5
x=+/-.5+1.5
x=1; x=2

c)Solve by using the quadratic formula. 
Show work in this space. 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=-3, c=2
{{{(-(-3)+- sqrt(-3^2-4*1*2))/(2*1)}}}
{{{(3+-sqrt(9-8))/2}}}
{{{3+-sqrt1)/2}}}
{{{3+1/2}}}
{{{3-1/2}}}
{{{(4/2)=2}}}
{{{(2/2)=1}}}
so; 
x=2 or x=1
=)