need help in rewrting

[Summer01]

D)8x-4=±?-32
E)8x-4=?-32 then x=(4+?-32)/8
F)2x-2=-?-32 then x=(4-?-32)/8

and

D)?(4x^2-8x+4)=±?56
E)2x-2=?56 then x=(2+?56)/2=1+?14
F)2x-2=-?56 then x=(2-?56)/2=1-?14



I just need to rewrite D, E & F in more layman terms not with / and ?
Thank-you

 

[mmm4444bot]

Start by simplifying the radical.

\(\displaystyle \sqrt{-32}\)

\(\displaystyle \sqrt{(-1)(2)(16)}\)

\(\displaystyle \sqrt{-1} \cdot \sqrt{2} \cdot \sqrt{16}\)

\(\displaystyle i \cdot \sqrt{2} \cdot 4\)

Now you have two equations to solve:

\(\displaystyle 8x \ - \ 4 \ = \ 4\sqrt{2} \ i\)

and

\(\displaystyle 8x \ - \ 4 \ = \ -4\sqrt{2} \ i\)

I would factor 4 out of the lefthand side, before dividing.

Can you finish?

Do the second exercise the same way.

 

[Summer01]

Thank-you mmm4444bot for your help
But this is the answer to my problem I already did the work I just want to reword it without using / ?

 

[mmm4444bot]

The first equation has two solutions:

\(\displaystyle x \ = \ \frac{1}{2} \ + \ \frac{\sqrt{2}}{2} \ i\)

OR

\(\displaystyle x \ = \ \frac{1}{2} \ - \ \frac{\sqrt{2}}{2} \ i\)

?

I already did the work I just want to reword it without using / ?

You're asking how to write the Rational number 1/2 without using a fraction bar? If so, you could express it as a decimal.

You're asking how to write the square root of 2 without using a radical sign? If so, you could switch to exponential notation.

The solutions are:

\(\displaystyle x \ = \ 0.5 \ + \ 0.5(2^{0.5}) \ i\)

OR

\(\displaystyle x \ = \ 0.5 \ - \ 0.5(2^{0.5}) \ i\)

If approximations are okay, you could evaluate and round ?2/2.

The solution approximations are:

\(\displaystyle x \ \approx \ 0.5 \ + \ 0.7071 \ i\)

OR

\(\displaystyle x \ \approx \ 0.5 \ - \ 0.7071 \ i\)

Why do you want to avoid using the symbols / and ? ?

 

[Summer01]

Thanks again mmm4444bot this is a big help. Now would say that these two problems are imaginary number (answers)
To answer your question I must write this out by teacher's request long handed.

 

[Denis]

To answer your question I must write this out by teacher's request long handed.

/ = divided by
other one = square root of

S'that long enough? :shock:

 

[mmm4444bot]

I must write this out by teacher's request long handed.

And any symbols are forbidden? Good grief! Is your teacher Robert Mugabe?

"The solutions for x are the ratio one over two plus or minus the imaginary unit i times the ratio square root of 2 over 2."

:roll:

 

[Summer01]

Thanks mmm4444bot,
In my last post I was just answering you about why I was not using symbols.

And then I was asking another question about imaginary numbers because I am little confused about them yet. So I was wondering if these problems had them.
My teacher is very nice she just wants us to do it this way first and then we will go on to symbols.
Thanks again for being so patient with me