How do you solve #0 = x^2 - 5x + 6# using the quadratic formula?

1 Answer
Mar 30, 2016

Answer:

#x=3,2#

Explanation:

#color(blue)(0=x^2-5x+6#

Rewrite in standard form

#rarrcolor(purple)(x^2-5x+6=0#

This is a Quadratic equation (in form #ax^2+bx+c=0#)

Use Quadratic formula

#color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)#

Remember that #a,bandc# are the coefficients of #x^2,xand6#

Now,

#color(red)(a=1,b=-5,c=6#

#rarrx=(-(-5)+-sqrt(-5^2-4(1)(6)))/(2(1))#

#rarrx=(5+-sqrt(-5^2-4(1)(6)))/(2)#

#rarrx=(5+-sqrt(25-4(1)(6)))/(2)#

#rarrx=(5+-sqrt(25-(24)))/(2)#

#rarrx=(5+-sqrt(1))/(2)#

#rarrx=(5+-1)/(2)#

Now we have #2# solutions for #x#

#color(purple)(x=(5+1)/(2)=6/2=3#

#color(orange)(x=(5-1)/(2)=4/2=2#

#color(blue)( :.ul bar| x=2,3|#