Question

complete the square?


3x^2 + 7x - 12

Answer 1

Hint: It's usually easier for me if I divide everything by what's in front of the x^2 first

Answer 2

x^2 + (7/3)x - 12/3
x^2+(7/3)x-4
What's half of (7/3)?

Answer 3

(7 / 3) / 2 = 1.16666667

Answer 4

Probably easier to keep it as a fraction, \(\dfrac{7}{6}\)

Answer 5

Remember, (x+a)^2=x^2+2ax+a^2
We need to add "a^2" to this expression (as well as subtract it)

Answer 6

remember, a=7/6

Answer 7

Square it to complete the square, \(\left(\dfrac{7}{6}\right)^2=\dfrac{7^2}{6^2}\)

Answer 8

so wouldn't it be x^2 + 7/4x=4?

Answer 9

\(x^2+\dfrac{7}{3}x=4\), but now we need to do the actual completing the square part, which is to add and subtract our squared constant. So, \(x^2+\dfrac{7}{3}x+\dfrac{49}{36}-\dfrac{49}{36}=4\), or if you prefer, \(x^2+\dfrac{7}{3}x+\dfrac{49}{36}=4+\dfrac{49}{36}\). Now we can factor the left side.

Answer 10

ohhh okay. got it, thanks.