Question

Please HElP.. The product of a number and the number increased by 9 is 15. What is the larger of the 2 solutions?

Answer 1

let the number be x then the number increased by 9 is (x+9) and since their product is 15,
x*(x+9) =15
solve for x and get the larger value

Answer 2

do i distrubute that ??? @sauravshakya

Answer 3

yes

Answer 4

Yes distribute the 'x' into the parenthesis

Answer 5

so its 9x ??

Answer 6

x times x = ?

x times 9 = ?

Answer 7

0

Answer 8

No....when you distribute the 'x' into the parenthesis...you multiply the x by each term in the parenthesis..

x(x + 9)

means

(x times x) + (x times 9)

so first...what is x times x?

Answer 9

idk wouldnt be x?

Answer 10

Not quite...

\[\large x \times x = x^2\]

Answer 11

oh right.

Answer 12

9x is the next one ?

Answer 13

Yeah...so now that and 9 times x = 9x

means we have

\[\large x^2 + 9x = 15\]

now we have a quadratic...can you solve this?

Answer 14

do i solve itl ike that or use a formula ??..

Answer 15

You can either use the "completing the square method" or use the quadratic formula...which would you like to do?

Answer 16

quadratic formula

Answer 17

Good because the completing the square would have gotten messy quick lol

Do you know the quadratic formula??

Answer 18

"ax^2 + bx + c = 0"

Answer 19

is this it

Answer 20

That is the form you would use....so good lets start with that...your equation is

\[\large x^2 + 9x = 15\]

How do you make that look like

\[\large ax^2 + bx + c = 0\]

?

Answer 21

x+9=15 ?

Answer 22

Not quite...the only difference between your equation and the form we need is that the form we need is = to 0....yours is = to 15...

so to change your equation ...into one that is = to 0....we just subtract 15 from both sides of the equation

\[\large x^2+ 9x - 15 = 15 - 15\]

simplified down it is...

\[\large x^2+ 9x - 15 = 0\]

Now...compare that to the form that we wanted...

\[\large ax^2 + bx + c\]

What are you 'a' 'b' and 'c' values?

Answer 23

a=x b=9 c=-15

Answer 24

ohhh so close...a = 1...remember those values are the coefficients of the variables....so ax² ....the a = 1...because it is just 1x² right?

so

a = 1, b = 9, and c = -15

Okay?

Answer 25

NOW...we use the quadratic formula

\[\huge \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]

Just substitute the values you have for 'a' 'b' and 'c' into this equation...

Answer 26

that sign next to -b how do you put that in the calc ? and is x always 1 ??

Answer 27

Dont worry about that sign for the moment...you'll see what that does soon...

I'll put all the values in for you and show you...

\[\huge \frac{ -9 \pm \sqrt{9^2 - 4(1)(-15)} }{ 2(1) }\]

Now...we simplify...

Answer 28

\[\huge \frac{ -9 \pm \sqrt{81 + 60} }{ 2 }\]

Answer 29

This now becomes

\[\huge \frac{ -9 \pm \sqrt{141} }{ 2 }\]

Answer 30

What you do now...is you seperate this into 2 equations...this is what that +/- sign does...

This becomes...

\[\huge \frac{ -9 + \sqrt{141} }{ 2 } = \space ?\]

and

\[\huge \frac{ -9 - \sqrt{141} }{ 2 } = \space ?\]

Answer 31

-3.062828956 for the first oneee ??

Answer 32

and -14.93717104 for the 2nd..

Answer 33

hmm...not quite what I get...

\[\huge \sqrt{141} = 11.8743420870\]

so

\[\huge \frac{ -9 + 11.8743420870 }{ 2 } = ?\]

and

\[\huge \frac{ -9 = 11.8743420870 }{ 2 } = ?\]

Answer 34

Argh typo there...the '=' in the second is supposed to be a '-'

Answer 35

So I get

1.4371710435 for the first one...

and

-10.437171043 for the second one...so which is the largest of the 2?

Answer 36

the first one thats positive ??

Answer 37

Mmhmm :) that would be correct!

Answer 38

ok but i don't think thats the final abswer that long decimal ??

Answer 39

so should i just put 1 ??

Answer 40

You're most likely right lol...but no I wouldn't round it down to 1...I would keep maybe 2 decimal places 1.44 I would say ...but just so we're clear...this is an approximate answer

If we could I would have kept it at

\[\large \frac{ -9 + \sqrt{141} }{ 2 }\]

But if we want a decimal..then yeah do 1.44

Answer 41

Its wrong :(

Answer 42

Well it is right...just must be because we rounded....because if you plug in the actual thing we got...the (-9 + √141)/2 into your equation...you get 15

maybe you should put the full decimal then...

1.437171043518959

Answer 43

it said this when i got it wrong Translate to an equation. Get the equation equal to 0 before solving.

Answer 44

Right...we did that...remember...we make your equation = 0 and we got all the way to here...

Answer 45

yes i remember that ... but why is it wrong. /:

Answer 46

we have the right answer...it must just be because we rounded oddly....it should be either that final equation we got...

\[\large \frac{ -9 + \sqrt{141} }{ 2 }\]

or the decimal equivalency of that...1.437171043518959

Answer 47

did we translate this into an equation ? and trust me it will mark it wrong if i put that long number there

Answer 48

i only have 2 more attempts to get this right

Answer 49

mmhmm....translate into equation is where we went from the words to the x(x + 9) = 15 thing...

Answer 50

Then set the equation = to 0 is where we distributed and subtracted 15 from both sides remember and ended up with

x² + 9x - 15 = 0

Answer 51

I'm telling you ....we have the correct answer....just don't know how the answering service wants the answer...

Answer 52

Your right did we do any of this ? Short answer questions are very particular on how to enter answers so they are graded correctly. Read the question carefully to ensure you answer the question being asked.

Here are some tips to increase the chance of the short answer questions that follow be graded correctly.

Don't include spaces. Such as x + 3 may be marked wrong but x+3 is correct.
Don't include symbols. Such as $25 is wrong but 25 is correct.
2x is correct but 2*x or 2(x) are marked wrong.
If the question asks for an expression, then = is never used.
If the question asks for an equation, then = must be used.
Don't round unless stated to do so in the problem.
If the answer is a fraction, write the fraction instead of decimal unless the problem states otherwise.
Always write in descending order, unless the problem specifies otherwise.

Answer 53

"If the answer is a fraction, write the fraction instead of decimal unless the problem states otherwise"

This leads me to believe they want something like what we got...


\[\large \frac{ -9 + \sqrt{141} }{ 2 }\]

Answer 54

I think they would want just a whole number

Answer 55

"Don't round unless stated to do so in the problem. "

I don't think so..ugh what an annoying service lol

Answer 56

tell me about it had to deal with this forever lol

Answer 57

Haha...idk I'm thinking it wants the fraction somehow idk lol it's annoying as anything but...

Answer 58

i took a practice test on this and there were no fractions!!! They were either whole numbers or decimals like this 1.6

Answer 59

should i try 1.43

Answer 60

Lol Well idk...if you want to try 1 like you were saying...then good luck xD haha I don't know what they want...

and no definietly not....1.437 does not go to 1.43....argh this is terrible....

Answer 61

why wouldn't 1.43 be right & its okay I'll figure it out.

Answer 62

Well because...the full number is 1.437.....etc.... you would be rounding up....you cannot just cut off after the 3....the 7 DOES have an effect on that 3....it would make it round up......I know the question says don't round but....if that were the case then 1.4 would be correct to....idk

Answer 63

maybe it is 1.4