SOLUTION: I'm trying to help my granddaughter. I'm stumped p-4/9p = -7/9

Algebra ->  Equations -> SOLUTION: I'm trying to help my granddaughter. I'm stumped p-4/9p = -7/9      Log On


   

Question 177079: I'm trying to help my granddaughter. I'm stumped
p-4/9p = -7/9
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
I think you mean:
%28p-4%29%2F9p+=+-7%2F9
multiply both sides by 9p:
%28p-4%29+=+-7p
add 7p to both sides:
6p-4+=+0
add 4 to both sides:
6p+=+4
divide both sides by 6:
p+=+4%2F6
reduce to get:
p+=+2%2F3
.
.
.
BUT, if you mean:
p-4%2F9p+=+-7%2F9
multiply both sides by 9p:
9p%5E2-4+=+-7p+
add 7p to both sides:
9p%5E2%2B7p-4+=+0+
Here, you have to use the quadratic equation to solve.
Doing so will yield:
p = {0.383, -1.161}
Details are below:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ap%5E2%2Bbp%2Bc=0 (in our case 9p%5E2%2B7p%2B-4+=+0) has the following solutons:

p%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=%287%29%5E2-4%2A9%2A-4=193.

Discriminant d=193 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+193+%29%29%2F2%5Ca.

p%5B1%5D+=+%28-%287%29%2Bsqrt%28+193+%29%29%2F2%5C9+=+0.382913554969434
p%5B2%5D+=+%28-%287%29-sqrt%28+193+%29%29%2F2%5C9+=+-1.16069133274721

Quadratic expression 9p%5E2%2B7p%2B-4 can be factored:
9p%5E2%2B7p%2B-4+=+9%28p-0.382913554969434%29%2A%28p--1.16069133274721%29
Again, the answer is: 0.382913554969434, -1.16069133274721. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B7%2Ax%2B-4+%29

.