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):

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