SOLUTION: Please help me solve this Quadratic equation. 9x^2+6x-4=0 I have solved it down to -6 sqrt 180 / 18. this is also the same as your sight gave me, but the answer key says t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this Quadratic equation. 9x^2+6x-4=0 I have solved it down to -6 sqrt 180 / 18. this is also the same as your sight gave me, but the answer key says t      Log On


   

Question 223760: Please help me solve this Quadratic equation.
9x^2+6x-4=0
I have solved it down to -6 sqrt 180 / 18.
this is also the same as your sight gave me, but the answer key says this.
-1 sqrt 5 / 5
Found 3 solutions by brich, drj, edjones:
Answer by brich(7) About Me  (Show Source):
You can put this solution on YOUR website!
Do you know the quadratic formula?
It appears that you do.
your sqr_root(180) reduces to 6sqr_root(5) by the way
so now you have:
[-6(+/-)6sqr_root(5)]/18
pull/factor a 6 out of the numerator
6[-1(+/-)sqr_root(5)]/18
6/18 reduces to 1/3
so the final answer i'm coming up with and you seem to already have is:
[-1(+/-)sqr_root(5)]/3
I appears as if the answer key is incorrect
Your answer appears correct but make sure you simplify like I pointed out
That all
I hope that was helpful
Let me know if you are still confused

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this Quadratic equation.

9x%5E2%2B6x-4=0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B6x%2B-4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A9%2A-4=180.

Discriminant d=180 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+180+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+180+%29%29%2F2%5C9+=+0.412022659166597
x%5B2%5D+=+%28-%286%29-sqrt%28+180+%29%29%2F2%5C9+=+-1.07868932583326

Quadratic expression 9x%5E2%2B6x%2B-4 can be factored:
9x%5E2%2B6x%2B-4+=+9%28x-0.412022659166597%29%2A%28x--1.07868932583326%29
Again, the answer is: 0.412022659166597, -1.07868932583326. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B6%2Ax%2B-4+%29



x1=%28-6%2Bsqrt%28180%29%29%2F18 and x1=%28-6-sqrt%28180%29%29%2F18

So, you are in the right track.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J





Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
[-6+-sqrt(180)]/18 is what you got NOT what you posted.
=[-6+-sqrt(36*5)]/18
=[-6+-6sqrt(5)]/18
=[-1+-sqrt(5)]/3 better
.
Ed