SOLUTION: Hi, I tried to solve for 5x^2=3x+2 and thought the answer is x=2/5 and x=-2. Also, I tried to solve 3x^3 +2x^2=x and came up with x=0, 1/3, -1. I am not sure of these answers.

Algebra ->  Algebra  -> Exponents -> SOLUTION: Hi, I tried to solve for 5x^2=3x+2 and thought the answer is x=2/5 and x=-2. Also, I tried to solve 3x^3 +2x^2=x and came up with x=0, 1/3, -1. I am not sure of these answers.       Log On

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Question 120450: Hi, I tried to solve for 5x^2=3x+2 and thought the answer is x=2/5 and x=-2.
Also, I tried to solve 3x^3 +2x^2=x and came up with x=0, 1/3, -1. I am not
sure of these answers. Can you please help me? Thank you!
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
#1


5x%5E2=3x%2B2 Start with the given equation


0=3x%2B2-5x%5E2 Subtract 5x^2 from both sides.


0=-5x%5E2%2B3x%2B2 Rearrange the terms.


0=-%28x-1%29%285x%2B2%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-1=0 or 5x%2B2=0

x=1 or x=-2%2F5 Now solve for x in each case


So our answer is
x=1 or x=-2%2F5


Notice if we graph y=-5x%5E2%2B3x%2B2 we can see that the roots are x=1 and x=-2%2F5 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+-5x%5E2%2B3x%2B2%29+





#2


3x%5E3%2B2x%5E2=x Start with the given equation


3x%5E3%2B2x%5E2-x=0 Subtract x from both sides.




x%28x%2B1%29%283x-1%29=0 Factor the left side


Now set each factor equal to zero:
x=0, x%2B1=0 or 3x-1=0

x=0, x=-1 or x=1%2F3 Now solve for x in each case


So our answer is
x=0, x=-1 or x=1%2F3


Notice if we graph y=3x%5E3%2B2x%5E2-x we can see that the roots are x=0, x=-1 and x=1%2F3. So this visually verifies our answer.


+graph%28500%2C500%2C-5%2C5%2C-5%2C5%2C0%2C+3x%5E3%2B2x%5E2-x%29+