Question

(x)^2+(1/2x+11)^2=(2x+1)^2
PLEASE HELP

Answer 1

\[(x)^2+(\frac{ 1 }{ 2 }x+11)^2=(2x+1)^2\]

Answer 2

Expand the expressions to get
\( -\frac{11}{4}x^2+7x+120=0 \)
Solve for x.

Answer 3

http://statisticslectures.com/images/trinomial11.gif

Answer 4

x^2= -480/11

Answer 5

I have a negative fraction and a positive integer as the two possible answers.

Answer 6

how did you get that @mathmate

Answer 7

\[x ^{2}+\frac{ 1 }{ 4}x ^{2}+2*\frac{ 1 }{ 2}x*11+121=4x ^{2}+2*2x*1+1^{2}\]
\[x ^{2}+\frac{ 1 }{ 4 }x ^{2}+11x+121-4x ^{2}-4x-1=0\]
\[-3x ^{2}+\frac{ 1 }{ 4 }x ^{2}+7x+120=0\]
\[-12x ^{2}+x ^{2}+28x+120=0\]
\[11x ^{2}-28x-120=0\]
\[x=\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\]
a=11, b=-28,c=-120
calculate for x

Answer 8

@surjithayer I believe c should be -480. You probably forgot to multiply 120 by -4.

Answer 9

im confused, could you maybe write down the stps?

Answer 10

yes you are right
c=-480

Answer 11

@surjithayer
wrote down all the steps, the last equation should read
\( 11x^2 -28x-480=0 \)
from which you can solve for the unknowns using the quadratic formula surjithayer supplied.

Answer 12

how did you get that out of \[x^2+(1/2x+11)^2=(2x+1)^2\]

Answer 13

by expansion using the identity on each of the three terms:
\((a+b)^2 = a^2 + 2ab + b^2 \)
but watch the signs.

Answer 14

could you explain that more please? im still confused

Answer 15

correction
\[-12^{2}+x ^{2}+28x+480=0\]
\[11x ^{2}-28x-480=0\]
now you can use the formula given above.

Answer 16

im so confused. this is what i did.
\[x^2+(\frac{ 1 }{ 2 }+11)^2=(2x+1)^2\]\[x^2+\frac{ 1 }{ 2 }x^2+121=4x^2+1\]\[-\frac{ 11 }{ 4 }+120=0\]

Answer 17

oh sorry \[\frac{ -11 }{ 4}x^2+120=0\]

Answer 18

@mathmate @surjithayer

Answer 19

You have missed out the cross terms (2ab) in the identity:
\( (a+b)^2=a^2+2ab+b^2 \)
If you put those in, you will get exactly the same answer as surjithayer did.

Answer 20

so how do i get from where i am to your guys's answer

Answer 21

I think @surjithayer is working on it. It'll be worth the wait!

Answer 22

\[X=\frac{ +28\pm \sqrt{\left( -28 \right)^{2}-4*11*-480} }{ 2*11 }\]

\[x=\frac{ 28\pm \sqrt{784+21120} }{ 22 }\]
\[x=\frac{ 28\pm \sqrt{21904} }{22 }=\frac{ 28\pm148 }{22 }=\frac{ 170 }{22 },\frac{ -120 }{ 22 }\]
now you can find

Answer 23

i dont think thats correct, i have an answer key but it just doesnt have the work. the answers are * and -60/11

Answer 24

@surjithayer

Answer 25

His work is correct up to \( \frac{28\pm 148}{22} \).
He probably meant for you to check his work.
Start from there and get your final answer.