Question

will you Check my answer please? It is about the quadratic formula! (you will have to give me a min to draw it.)

Answer 1

I got \[9+5\sqrt{29} ~~and~~ 9-5\sqrt{29}\]

Is that the final answer or can it be simplified to \[\sqrt{29} ~~and~~ -\sqrt{29}\]

Answer 2

the problem is \[7r^2-9r-23=0\]

Answer 3

it looks like you forgot to divide by (2a) which is 2*7 = 14 in this problem
\[ x = \frac{ 9 \pm 5\sqrt{29}}{14} \]

Answer 4

I was just about to type that into my questionxD I forgot to put it on here my bad haha

Answer 5

I have it all worked out on paper, I just did not enter it right on here on accident xD

Answer 6

you can use a calculator and change both expressions to decimals
and no, neither root can be simplified to sqr(29) (which you can also change to a decimal if you want to compare it to the roots)

Answer 7

i didn't know if the 9+5 (14) could be divided by the bottom 14 or not

Answer 8

the approximate value of the roots are
-1.2804 and 2.5661

sqr(29) is about 5.385

Answer 9

oh okay! thank you Phi !

Answer 10

**i didn't know if the 9+5 (14) could be divided by the bottom 14 or not**
do you mean 9 + 5 * sqr(29) ?
yes , you can divide that by 14: you write a line under it, then 14 under the whole thing
\[ \frac{9+5\sqrt{29}}{14} \]
if you like, practice changing that into a decimal
using a calculator.

Answer 11

so if I add (on the top) 5+19 that would become 14 sqrt 20 / 14 can the top 14 and the bottom 14 cancel each other out ? @phi

Answer 12

you don't have 5+19 up top, you have
\[ 9 + 5 \sqrt{29}\]
and that is divided by 14 : \( \frac{9 + 5 \sqrt{29}}{14}\)
It really can't be simplified (except to write an *approximate* decimal value)

The reason why is this:

First, remember sqrt(29) is a number (a bit larger than 5)
so this problem is the same "form" as for example
1+2*3 all divided by 2: \( \frac{1+2\cdot 3}{2} \)
you would not add 1+2 (I hope!). Order of operations says we do multiplies first.

anyway, it would not turn into 3*3/2 = 9/2
it is (1+6)/2 = 7/2