Question

what are the roots of this quadratic equation??

Answer 1

\[2(x + 3)^{2} = 5(x + 3)\]

Answer 2

-3 and -1/2

Answer 3

clear how to do it or no?

Answer 4

not really :P could you explain how to get to the answer?

Answer 5

you have a choice. you can multiply out, combine like terms and then solve a quadratic equation, or you can thing of
\[(x+3)=z\] and solve a quadratic in z. which do you choose?

Answer 6

we can even do both if you like, because this is the last one i do before lunch

Answer 7

just do which ever one is easiest:P

Answer 8

ok lets replace
\[x+3\] by \[z\] to get
\[2z^2=5z\]
\[2z^2-5z=0\]
\[z(2z-5)=0\]

Answer 9

so far so good?

Answer 10

yup

Answer 11

the solution are
\[z=0\] or
\[2z-5=0\]
\[2z=5\]
\[z=\frac{5}{2}\]

Answer 12

now we replace z by x + 3 to get the two answers
\[x+3=0\]
\[x=-3\]

Answer 13

or
\[x+3=\frac{5}{2}\]
\[x=\frac{5}{2}-3=-\frac{1}{2}\]

Answer 14

that's the answer i wrote on my test, and it was marked as wrong.. i said the zeros were ( 0, -3)

Answer 15

ahh but those were the zeros from z not from x+3

Answer 16

you have to go back and replace z by x+3 because that was the problem.

Answer 17

okay, thanks :]

Answer 18

if this is annoying you can just go ahead and multiply out:
\[2(x+3)^2=5(x+3)\]
\[2(x^2+6x+9)=5x+15\]
\[2x^2+12x+18=5x+15\]
\[2x^2+7x+3=0\]
\[(2x+1)(x+3)=0\]
etc