Question

please explain in steps :))

Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

3x2 – 48x + 153 = 0

Answer 1

first divide all by 3
what do you get?

Answer 2

you said "steps" right, that is step one

Answer 3

3,12, and 51

Answer 4

?

Answer 5

no, divide all the coefficents by 3
if it is not clear what i mean, i will show you

Answer 6

im sorry im not understanding ive never done the problem so i dont understand where to start :(

Answer 7

if you divide everything by 3, you have \(3\div 3=1,48\div 3=16,153\div 3=51\)
giving you \[x^2-16x+51=0\] that is the first step

Answer 8

ooooh ok i did divided by 3 i just didnt know what to do with the numbers

Answer 9

so ready for next step?

Answer 10

yup

Answer 11

subtract \(51\) from both sides and get
\[x^2-16x=-51\]

Answer 12

next?

Answer 13

what is half of \(16\) ?

Answer 14

8

Answer 15

ok so we write
\[(x-8)^2=-51+?\] now for the \(?\) what is \(8^2\) ?

Answer 16

16?

Answer 17

im sorry i dont understand

Answer 18

no dear, \(8^2\) not \(2\times 8\)

Answer 19

i.e. \(8\times 8\)

Answer 20

oh ok

Answer 21

let me know when you get \(64\)

Answer 22

then write
\[(x-8)^2=-51+64\] and \(64-51=13\) so this is
\[(x-8)^2=13\] with me so far? at the end i can rewrite all the steps so you have them all in one place if you like

Answer 23

yup oh and if you could do that i would be so happy cuz i have more problems like this one and im gonna use it asan example

Answer 24

ok we are not done yet, but almost
once we have
\[(x-8)^2=13\] you write
\[x-8=\pm\sqrt{13}\] then add \(8\) to get
\[x=8\pm\sqrt{13}\]

Answer 25

now i write all the steps for this one

Answer 26

\[3x2 – 48x + 153 = 0\] divide by 3 to make the "leading coefficient 1" and get
\[x^2-16x+51=0\] subtract \(51\) get
\[x^2-16=-51\] half of \(16\) is \(8\) and \(8^2=64\) write
\[(x-8)^2=-51+64=13\] take the square root of both sides, don't forget the \(\pm\) and get
\[x-8=\pm\sqrt{13}\] add \(8\) to get \(x\) by itself and finish with
\[x=8\pm\sqrt{13}\]

Answer 27

thank you alot

Answer 28

yw, hope the steps are more or less clear