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

1 Answer
Apr 7, 2018

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!