anonymous
  • anonymous
What are the solutions of x^2 - 3x +9 = 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Imaginary
anonymous
  • anonymous
Thanks man.
anonymous
  • anonymous
Sarcastic? :( I didn't technically help you.

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anonymous
  • anonymous
Well not sarcastic i figured you were at least trying to help so i appreciate that. The problem is still confusing me though? :[
anonymous
  • anonymous
You can either work it out with the quadratic formula or completing the square, but the graph does not cross the x axis, so both solutions are imaginary.
anonymous
  • anonymous
But i did not get two solutions in the problem? :[ im just totally confused on how to solve it :/
anonymous
  • anonymous
OK one second:
anonymous
  • anonymous
\[x^2 - 3x + 9 = 0\] \[\iff \left(x-\frac{3}{2}\right)^2 - \left(\frac{3}{2}\right)^2 + 9 = 0\] \[\iff \left(x-\frac{3}{2}\right)^2 = -\frac{27}{4}\] \[\implies x-\frac{3}{2} = \pm \sqrt{\frac{-27}{4}}\]
anonymous
  • anonymous
Of course, you could equally just use the formula, but I think this way is more fun. Do you know how to carry on (mainly with the root) to get the imaginary/complex solution?
anonymous
  • anonymous
I do not.
anonymous
  • anonymous
Do you see how the working I posted works?
anonymous
  • anonymous
Yeahh.....
anonymous
  • anonymous
\[\sqrt{\frac{-27}{4}} = \sqrt{-1}\cdot\sqrt{\frac{27}{4}} = i\cdot\frac{3\sqrt{3}}{2}\]
anonymous
  • anonymous
Again, it may be more 'standard' and easier to repeat if you use the quadratic formula instead, but it would still need you to take the root of a negative number.

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