Question

Solve by using the Quadratic Formula.
6r^2-r=1

Answer 1

quadratic formula : \(\large \frac{-b \pm \sqrt{b^2-4ac}}{2a}\)

Answer 2

Start by subtracting -1 from both sides. You want to fit the format : \(ax^2 +by+c =0\)

Answer 3

okay, so 6r^2-r-1=0

Answer 4

and the quadratic can be factored

but the GQF is probably easiest

Answer 5

\[\color{blue}6r^2 -\color{red}r-\color{green}1=0\]\[\color{blue}ax^2 -\color{red}by +\color{green}c =0\] See how it fits this format?

Answer 6

Now we know a=6, b=-1, c = 1, we can plug these into our quadratic formula posted above.

Answer 7

i thought c was -1

Answer 8

Sorry, yes, c= -1.

Answer 9

\[ \frac{-b \pm \sqrt{b^2-4ac}}{2a} \implies \frac{-(-1) \pm \sqrt{(-1)^2 -4(6)(-1)}}{2(6)}\]

Answer 10

Are you able to simplify this?

Answer 11

okay

Answer 12

What did you get? :)

Answer 13

\[\frac{ 1\pm \sqrt{25} }{ 12 } = \frac{ 1\pm5 }{ 12 }\]

Answer 14

Good job :) Therefore you will get two answers: \(\frac{1-5}{12}\) and \(\frac{1+5}{12}\)

Answer 15

What do these simplify to?

Answer 16

1/2 and - 1/3

Answer 17

Good job! you got it :)