Question 155070
IF IT'S ANY CONSOLATION, THERE'S CERTAINLY NOTHING WRONG WITH EITHER (being old and trying to help your daughter, that is)

Since this is a quadratic equation of the form Ax^2+Bx+C where C is zero, we should come up with two values for x.
4x^2+12x=0  looking at the left side, we can factor out a 4x and rewrite as follows:
4x(x+3)=0 now we have
4x=0
x=0
and
(x+3)=0 subtract 3 from each side
x+3-3=0-3
x=-3

So, our answers are x=0 and x=-3

CK
for x=0
4*0^2+12*0=0
0=0
and for x=-3
4*(-3^2)+12+(-3)=0 (note (-3^2)=+9
4*9-3*12=0
36-36=0
0=0

This problem could be solved using the quadratic formula:

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
Since C is zero, we would have:
{{{x = (-b +- sqrt( b^2))/(2*a) }}} or
{{{x = (-12 +- sqrt( -12^2 ))/(2*4) }}}
{{{x = (-12 +- sqrt(144))/(8) }}} 
{{{x = (-12 +or-12)/(8) }}} 
{{{x = (-12 +12)/(8) }}}
{{{x=0}}}
and 
{{{x = (-12 -12)/(8) }}}
{{{x = (-24)/(8) }}}
{{{x=-3}}} 

 


 

Hope this helps---ptaylor