Question #451c2

1 Answer
Mar 1, 2017

Answer:

#x=3/2+-sqrt(21)/2 larr" exact values"#

#x~~3.791" ; "x~~-0.791 larr" approximate values"#

Explanation:

#color(brown)("This part in great detail to demonstrate first principles")#

Multiply everything inside the bracket by the #x# that is outside giving:

#" "3x-x^2" "=" "-3#

To make the #x^2# positive add #x^2# to both sides

#" "color(green)(3x-x^2color(red)(+x^2)" "=" "-3color(red)(+x^2)) #

But #-x^2+x^2=0#

#" "3x+0" "=" "x^2-3#

Subtract #color(red)(3x)# from both sides

#color(green)(" "3xcolor(red)(-3x)" "=" "x^2-3color(red)(-3x)#

#" "0" "=" "x^2-3x-3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Calculated much faster now")#

Standard form #->y=ax^2+bx+c#

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

#x=(-(-3)+-sqrt((-3)^2-4(1)(-3)))/(2(1))#

#x=3/2+-sqrt(9+12)/2#

#x=3/2+-sqrt(21)/2 larr" exact values"#

#x~~3.791" ; "x~~-0.791#

Tony B