SOLUTION: Please Help!!! Thanks Solve in the quadratic method and one other method. factoring, property of sq., or completing the square Show work. 3x^2 = 2x + 5

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please Help!!! Thanks Solve in the quadratic method and one other method. factoring, property of sq., or completing the square Show work. 3x^2 = 2x + 5      Log On


   

Question 203249This question is from textbook
: Please Help!!! Thanks Solve in the quadratic method and one other method. factoring, property of sq., or completing the square Show work.
3x^2 = 2x + 5 This question is from textbook

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+=+2x+%2B+5
3x%5E2+-+2x+-5+=+0
%283x-5%29%28x%2B1%29=0
so either (3x-5)=0 or (x+1)=0 , which means roots are 5/3 and -1
Look here for lots of tools to help sove these types of problems
http://www.algebra.com/tutors/all-solvers.mpl
Using quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-2x%2B-5+=+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=%28-2%29%5E2-4%2A3%2A-5=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C3+=+1.66666666666667
x%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C3+=+-1

Quadratic expression 3x%5E2%2B-2x%2B-5 can be factored:
3x%5E2%2B-2x%2B-5+=+3%28x-1.66666666666667%29%2A%28x--1%29
Again, the answer is: 1.66666666666667, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-2%2Ax%2B-5+%29