sighn0more
  • sighn0more
Hello! Please help me work through and solve this problem (it requires the quadratic equation): (3x + 1) ^2 = -2x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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sighn0more
  • sighn0more
Do I need to expand the binomial first or does this problem require a different course?
freckles
  • freckles
yes
sighn0more
  • sighn0more
Okay, so that would get me to 9x^2 + 6x + 2 = -2x I think

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freckles
  • freckles
\[(3x+1)^2=(3x)^2+2(3x)(1)+1^2 \\ (3x+1)^2=9x^2+6x+1\]
freckles
  • freckles
so should be: \[9x^2+6x+1=-2x \\ \text{ then add } 2x \text{ on both sides } \\ 9x^2+6x+2x+1=0 \\ 9x^2+8x+1=0\]
sighn0more
  • sighn0more
Oh yes, sorry. Error on my part! And from here should these numbers be my values for a, b, and c?
freckles
  • freckles
yes 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
  • freckles
and after solving these equation I can tell you you will not have any domain issues with the answers you get
sighn0more
  • sighn0more
Perfect! I ended up getting -8 +- radical 28 / 18
sighn0more
  • sighn0more
I guess I would need to simplify this further...
freckles
  • freckles
\[x=\frac{-8 \pm \sqrt{28}}{18} \\ \text{ note : } \sqrt{28}=\sqrt{4 \cdot 7} =\sqrt{4} \sqrt{7}=2 \sqrt{7} \\ \] yes your solution can be simplified see the note as a hint
sighn0more
  • sighn0more
Oh, so my final answer would be x = -4/9 +- radical 7 / 9
freckles
  • freckles
\[x=\frac{-8 \pm 2 \sqrt{7}}{18} \\ \text{ divide \top and bottom by 2 } \\ x=\frac{\frac{-8}{2} \pm \frac{2}{2} \sqrt{7}}{\frac{18}{2}} \\ x=\frac{-4 \pm \sqrt{7}}{9} \\ \text{ yes this could be written as } x=\frac{-4}{9} \pm \frac{\sqrt{7}}{9}\]
sighn0more
  • sighn0more
Thank you!!! This helped a bunch.
freckles
  • freckles
cool stuff! :)

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