Question

Complete the square:
y = (x+6)(2x-5)

Answer 1

first foil,

\[x(2x)+x(-5)+6(2x)+6(-5)\]
\[2x^2-5x+12x-30\]

Answer 2

\[2x^2+7x-30\]

Answer 3

so 2x^2+ 7x - 30

which will take to: 2(x^2 +7/2x) - 30?

Answer 4

I just don't know what to do from here.

Answer 5

that would work yes

Answer 6

alright so first take the coefficient of the x value and divide it in half

Answer 7

7/4?

Answer 8

\[\frac{7}{2}*\frac{1}{2}\]

Answer 9

yes now square that

Answer 10

Oh god. This will be a big number.
49/16?

Answer 11

yep so now thats your second square.. aka b in (a+b)^2

so now if you add it into the parenthesis you have to subtract it on the outside so that you don't manipulate the equation . In otherwords

\[2(x^2+\frac{7}{2}x+\frac{49}{16})-30-\frac{49}{16}=0\]

Answer 12

so now you have a perfect square within the parenthesis

\[2(x+\frac{7}{4})^2-30-\frac{49}{16}=0\]

Answer 13

to simplify more you can turn the 30 into 16th's and add them together

Answer 14

don't you have to multiply 49/16 by 2?

Answer 15

yes you want to multiply that number by 2

Answer 16

it should look like this

\[2[(x+\frac{7}{4})^2-\frac{49}{16}]-30\]

Answer 17

so 90/16?
then from there it's
- 480/16 - 90/16

2(x + 7/2)^2 - 285/8

Answer 18

oh wait.

Answer 19

but then arent you multiplying the x by 2 which will make it 2x?

Answer 20

meh i'd leave it out if you're teacher doesn't mind

Answer 21

i'd just simplify the outside of the parenthesis and leave it as 2( )

Answer 22

Alright, i'll just wait for a solid answer. Thanks for the help :D