SOLUTION: Hi. I am having a hard time solving this problem algebraically and I would appreciate if you could assist me. The problem reads: {{{y=x^3-x^2}}} {{{y=5x^2}}}

Algebra ->  Systems-of-equations -> SOLUTION: Hi. I am having a hard time solving this problem algebraically and I would appreciate if you could assist me. The problem reads: {{{y=x^3-x^2}}} {{{y=5x^2}}}      Log On


   

Question 209454: Hi. I am having a hard time solving this problem algebraically and I would appreciate if you could assist me. The problem reads:
y=x%5E3-x%5E2
y=5x%5E2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E3-x%5E2 Start with the first equation.


5x%5E2=x%5E3-x%5E2 Plug in y=5x%5E2


0=x%5E3-x%5E2-5x%5E2 Subtract 5x%5E2 from both sides.


0=x%5E3-6x%5E2 Combine like terms.


0=x%5E2%28x-6%29 Factor out the GCF x%5E2


x%5E2=0 or x-6=0 Use the zero product property to set each factor equal to zero.


x=0 or x=6 Solve for 'x' in each equation.


So the solutions are x=0 (with a multiplicity of 2) or x=6