SOLUTION: HAVING PROBLEMS SOLVING QUADRATIC EQUATIONS INVOLVING FRACTIONS E.G 4 OVER 2X-3 - 2 OVER X = 1 OVER NINE. THANKS FOR YOUR HELP

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: HAVING PROBLEMS SOLVING QUADRATIC EQUATIONS INVOLVING FRACTIONS E.G 4 OVER 2X-3 - 2 OVER X = 1 OVER NINE. THANKS FOR YOUR HELP       Log On


   

Question 220965: HAVING PROBLEMS SOLVING QUADRATIC EQUATIONS INVOLVING FRACTIONS E.G
4 OVER 2X-3 - 2 OVER X = 1 OVER NINE.
THANKS FOR YOUR HELP
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
HAVING PROBLEMS SOLVING QUADRATIC EQUATIONS INVOLVING FRACTIONS E.G
4 OVER 2X-3 - 2 OVER X = 1 OVER NINE.

4%2F%282x-3%29-2%2Fx=1%2F9

Step 1. To get rid of fractions multiply by 9x(2x-3) to both sides of the equation:

9x%282x-3%29%2A4%2F%282x-3%29-9x%282x-3%29%2A2%2Fx=9x%282x-3%29%2A1%2F9

36x-18%282x-3%29=9x%282x-3%29

36x-36x%2B54=18x%5E2-27x

Step 2. Subtract54 to both sides of the equation:

54-54=18x%5E2-27x-54

0=18x%5E2-27x-54

0=2x%5E2-3x-6

Step 3. Solving using the quadratic formula yields

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=2, b=-3, and c=-6

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-6+=+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=%28-3%29%5E2-4%2A2%2A-6=57.

Discriminant d=57 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+57+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+57+%29%29%2F2%5C2+=+2.63745860881769
x%5B2%5D+=+%28-%28-3%29-sqrt%28+57+%29%29%2F2%5C2+=+-1.13745860881769

Quadratic expression 2x%5E2%2B-3x%2B-6 can be factored:
2x%5E2%2B-3x%2B-6+=+2%28x-2.63745860881769%29%2A%28x--1.13745860881769%29
Again, the answer is: 2.63745860881769, -1.13745860881769. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-6+%29



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