Falling_In_Katt
  • Falling_In_Katt
***WILL MEDAL*** Solve this equation by completing the square. 3x^2 - 4x = -2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ChillOut
  • ChillOut
Do you know the steps to complete the square?
Falling_In_Katt
  • Falling_In_Katt
no...
ChillOut
  • ChillOut
All right. Here you go. Divide the whole equation by whatever is multiplying the squared term. In this cae you have to divide everything by 3. By doing this, you have \(x^{2}-\frac{4}{3}x=\frac{-2}{3}\)

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ChillOut
  • ChillOut
Then you take half of the "x" coefficient (\(\frac{4}{3}\)), square it and add to both sides.
ChillOut
  • ChillOut
Which means you will be adding \((\frac{2}{3})^{2}\) to both sides.
ChillOut
  • ChillOut
By doing this, you will have \(x^{2}-\frac{4}{3}x+ \frac{4}{9}=\frac{-2}{3}+\frac{4}{9}\)
ChillOut
  • ChillOut
Do you see that the left side can be rewritten as a perfect square?
Falling_In_Katt
  • Falling_In_Katt
yes
ChillOut
  • ChillOut
And that's it! Rewrite the left side, simplify the right side and you will *ALMOST* have your answer. Can you finish it?
Falling_In_Katt
  • Falling_In_Katt
i can try
ChillOut
  • ChillOut
Take your chances :3
Falling_In_Katt
  • Falling_In_Katt
Im trying to square the left side and its not working
ChillOut
  • ChillOut
Well, rewriting it as a square we have \((x-\frac{2}{3})^{2}\)
ChillOut
  • ChillOut
check?
Falling_In_Katt
  • Falling_In_Katt
4/9?
ChillOut
  • ChillOut
Reminder that \((a-b)^{2}=a^{2}-2ab+b^{2}\) Moving on... We have \((x-\frac{2}{3})^{2}=\frac{-2}{9}\) and \(x-\frac{2}{3}=±\sqrt{\frac{-2}{9}}\) This problem WILL NOT have answers in the set of reals, ONLY in the set of complex numbers.
Falling_In_Katt
  • Falling_In_Katt
Oh. That makes more sense.
ChillOut
  • ChillOut
Does it ask for its roots?
Falling_In_Katt
  • Falling_In_Katt
No
ChillOut
  • ChillOut
Well, then there you have your answer. :D
Falling_In_Katt
  • Falling_In_Katt
Thank you

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