OpenStudy (starryknight):

please explain in steps :)) Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a. 3x2 ā€“ 48x + 153 = 0

OpenStudy (anonymous):

first divide all by 3 what do you get?

OpenStudy (anonymous):

you said "steps" right, that is step one

OpenStudy (starryknight):

3,12, and 51

OpenStudy (starryknight):

?

OpenStudy (anonymous):

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

OpenStudy (starryknight):

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

OpenStudy (anonymous):

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

OpenStudy (starryknight):

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

OpenStudy (anonymous):

so ready for next step?

OpenStudy (starryknight):

yup

OpenStudy (anonymous):

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

OpenStudy (anonymous):

next?

OpenStudy (anonymous):

what is half of \(16\) ?

OpenStudy (starryknight):

8

OpenStudy (anonymous):

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

OpenStudy (starryknight):

16?

OpenStudy (starryknight):

im sorry i dont understand

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (starryknight):

oh ok

OpenStudy (anonymous):

let me know when you get \(64\)

OpenStudy (anonymous):

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

OpenStudy (starryknight):

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

OpenStudy (anonymous):

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 \[x=8\pm\sqrt{13}\]

OpenStudy (anonymous):

now i write all the steps for this one

OpenStudy (anonymous):

\[3x2 ā€“ 48x + 153 = 0\] 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 \[x=8\pm\sqrt{13}\]

OpenStudy (starryknight):

thank you alot

OpenStudy (anonymous):

yw, hope the steps are more or less clear