Melody

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{53}} = {\frac{{\mathtt{11}}}{{\mathtt{3}}}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{1\,335}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{21}}\right)}{{\mathtt{6}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{1\,335}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{21}}\right)}{{\mathtt{6}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.089\: \!608\: \!635\: \!484\: \!241\: \!2}}{i}\right)\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.089\: \!608\: \!635\: \!484\: \!241\: \!2}}{i}\\
\end{array} \right\}$$

$$3x^2+21x+148=0\\\\
x=\frac{-21\pm\sqrt{1335}}{6}\qquad \mbox{That bit is correct}\\\\
\mbox{so it is only the coefficient of i that is in question}$$   

From my hand held casio calculator it is   6.089608635  so to 10 significant figures it is correct.

Okay, from further checking it appears to be correct to 12 significant figures the last 5 digits may have rounding error.

If you want an exact answer your would leave it as a surd.  

Now that depends on where there is.  there are many places that i am not.

I could turn this into a Cat-in-the-Hat saga.  I'm sure I could!

@@ End of Day Wrap - Thursday 29/5/14   Sydney, Australia   Time 23:50 pm 

Hi all,

It was a busy day today. All questions up to and including page 470, and all answers up to including page 1092 have been answered, checked, etc.  This means there are still some about for people to answer and/or check.

Our great answers today were provided by Rosala, Alan, GoldenLeaf, mjohnson, admin, zegroes, zacpac2020, reinout-g, Heureka, Rom and TakahiroMaeda.

Mjohnson and Zacpac2020 both only joined up yesterday - could have been today since I am ahead of almost everyone else!  Welcome to web2.0calc forum.  We all hope that you enjoy yourselves here!   

-------------------------------------------------------------

Now, there were lots of potentially interesting posts today and here are some of them.

Reinout-g is cracking jokes again - So what is new?

Alan's median is correct.

It is really good to remember that if there are n numbers, the middle position will be the (n+1)/2 position

In this example there are 6 numbers.  

The middle position is (6+1)/2=3.5  SO the median will be the average of the 3rd and 4th scores.

This is really handy knowledge when there are a lot of scores.

I already answered that today and so did Rom!

Just look around the forum and you will find your answer.  Here tis, I found it for you!

http://web2.0calc.com/questions/the-rule-of-a-table

You can just type in 'pi' too!  It's pretty cluey.

Remember GoldenLeaf, this is an approximation and you should state that but I've given you thumbs up.

sqrt(522) is an irrational number!

I really do not know what you mean.

do you mean the quadratic formula?

Here it is.

If      $$ax^2+bx+c=0$$

Look at the clip - remember that there should be an' $$x=$$' out the front.

Yes but Heureka, these are one number -NOT one digit!

$$\begin{array}{rll}
A&=&\pi r^2\\\\
15.89625&=&\pi r^2\\\\
\frac{15.89625}{\pi}&=&r^2\\\\
\sqrt{\frac{15.89625}{\pi}}&=&r\\\\
\end{array}\\\\
d=2r=2\sqrt{\frac{15.89625}{\pi}}\quad units$$

$${\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\frac{{\mathtt{15.896\: \!25}}}{{\mathtt{\pi}}}}}} = {\mathtt{4.498\: \!859\: \!201\: \!286\: \!069}}$$

diameter is approx 4.5 units