How do you solve # 3x^2 = -9x#?

1 Answer
Apr 7, 2018

Answer:

The two solutions are #x=0# and #x=-3#.

Explanation:

First, bring everything to one side of the equation:

#3x^2=-9x#

#3x^2color(blue)+color(blue)(9x)=-9xcolor(blue)+color(blue)(9x)#

#3x^2color(blue)+color(blue)(9x)=color(red)cancelcolor(black)(color(black)-9xcolor(blue)+color(blue)(9x))#

#3x^2+9x=0#

Now, divide by the common factor #3#:

#color(blue)(color(black)(3x^2+9x)/3)=color(blue)(color(black)0/3)#

#color(blue)(color(black)(color(red)cancelcolor(black)3x^2+color(red)cancelcolor(black)9^3x)/color(red)cancelcolor(blue)3)=color(blue)(color(black)0/3)#

#x^2+3x=color(blue)(color(black)0/3)#

#x^2+3x=0#

Now, use the distributive property backward to factor out the #x# term:

#color(red)x*color(blue)x+color(red)x*color(blue)3=0#

#(color(red)x)(color(blue)(x+3))=0#

Now, set each factor equal to #0# and solve for #x# in each one:

#color(white){color(black)( (color(red)x=0,qquadcolor(blue)(x+3)=0), (,qquadcolor(blue)x=-3):}#

These are the two solutions: #x=0# and #x=-3#. Hope this helped!