SOLUTION: How do you factor 1/2x^2+x-14/3=0?

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Question 357414: How do you factor 1/2x^2+x-14/3=0?
Found 2 solutions by ewatrrr, edjones:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Note:  first lets clear the denominators

 1/2x^2+x-14/3=0

Multiplying thru by 6

3x^2 + 6x -28 = 0

factoring using the quadradic formula

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

x+=+%28-6+%2B-+sqrt%28372+%29%29%2F%286%29+ 

x+=+-1+%2B-+sqrt%28372+%29%2F%286%29+ 

Calcutor makes short work of finding x

 x = 2.215 

x = -4.215

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
1/2x^2+x-14/3=0
3x^2+6x-28=0 multiply each side by 6.
x=-1-(sqrt(93)/3), x=-1+(sqrt(93)/3) see below.
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B6x%2B-28+=+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%2A3%2A-28=372.

Discriminant d=372 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+372+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+372+%29%29%2F2%5C3+=+2.21455025366432
x%5B2%5D+=+%28-%286%29-sqrt%28+372+%29%29%2F2%5C3+=+-4.21455025366432

Quadratic expression 3x%5E2%2B6x%2B-28 can be factored:
3x%5E2%2B6x%2B-28+=+3%28x-2.21455025366432%29%2A%28x--4.21455025366432%29
Again, the answer is: 2.21455025366432, -4.21455025366432. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B6%2Ax%2B-28+%29