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anonymous
 one year ago
Hello! Please help me work through and solve this problem (it requires the quadratic equation): (3x + 1) ^2 = 2x
anonymous
 one year ago
Hello! Please help me work through and solve this problem (it requires the quadratic equation): (3x + 1) ^2 = 2x

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do I need to expand the binomial first or does this problem require a different course?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so that would get me to 9x^2 + 6x + 2 = 2x I think

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[(3x+1)^2=(3x)^2+2(3x)(1)+1^2 \\ (3x+1)^2=9x^2+6x+1\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so should be: \[9x^2+6x+1=2x \\ \text{ then add } 2x \text{ on both sides } \\ 9x^2+6x+2x+1=0 \\ 9x^2+8x+1=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh yes, sorry. Error on my part! And from here should these numbers be my values for a, b, and c?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2yes you can use quadratic formula if you want a=9 b=8 c=1 in the end you should check your answers x being positive will not work just so you know because a real number squared will result in a positive number (or zero) (3x+1)^2=2x we need x to be negative because 0 obviously doesn't work either

freckles
 one year ago
Best ResponseYou've already chosen the best response.2and after solving these equation I can tell you you will not have any domain issues with the answers you get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Perfect! I ended up getting 8 + radical 28 / 18

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I guess I would need to simplify this further...

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[x=\frac{8 \pm \sqrt{28}}{18} \\ \text{ note : } \sqrt{28}=\sqrt{4 \cdot 7} =\sqrt{4} \sqrt{7}=2 \sqrt{7} \\ \] yes your solution can be simplified see the note as a hint

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, so my final answer would be x = 4/9 + radical 7 / 9

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[x=\frac{8 \pm 2 \sqrt{7}}{18} \\ \text{ divide \top and bottom by 2 } \\ x=\frac{\frac{8}{2} \pm \frac{2}{2} \sqrt{7}}{\frac{18}{2}} \\ x=\frac{4 \pm \sqrt{7}}{9} \\ \text{ yes this could be written as } x=\frac{4}{9} \pm \frac{\sqrt{7}}{9}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you!!! This helped a bunch.
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