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QUESTION: "I got on a test question that:

3x^2 - 2x + 7 = 0, then ( x - 1/3 )^2 = ???

The correct is -20/9. I don't see how this is possible since you get a negative number under the radical sign (-80) when using the quadratic formula.

Could you explain this? Thanks...."

ANSWER: Angelo,

This is a very good question. I have answered your question on a sheet of paper. I am attaching it herewith. Please let me know if anything is not clear or if you need additional information.

I hope this helps. All the best!

Regards,

Pawan

[an error occurred while processing this directive]---------- FOLLOW-UP ----------

QUESTION: Hello Pawan -- thanks for the solution. Naturally I gave you a rating of 10's across the board and "volunteer of the month."

I also received a different explanation I'd like for you to consider. He makes use of the "imaginary number." Tell me what you think of his method.

Try to get back to me> thanks .. Angelo

Angelo,

imaginary number (represented by i) is nothing but square root of -1. We too have imaginary number in our solution. If you see equation 3 in my solution, then you will see -5 under the square root sign. If we have to bring that '-' sign out of the square root, then that will be represented by 'i' and 'square root of -5' will become 'i * square root of 5'. I purposely avoided doing this because we have to anyway square this term at later step. Square of 'i' will be again -1 and hence I tried to keep it simple.

You may use imaginary number after equation 3 by adding a step there, if you wish.

I hope that this helps. Please let me know if you need further information on this.

All the best!

Regards,

Pawan

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I can answer Basic Mathematics questions like: Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc I can try to answer questions of probability and set theory

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I was 18th in High School Scholarship examination in Maharashtra State of India.
I was second in Mathematics in Maharashtra State in Secondary School Certificate examination.