SOLUTION: x+3squart root x-8=0

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: x+3squart root x-8=0      Log On


   

Question 76654: x+3squart root x-8=0
Answer by stargrl12566(16) About Me  (Show Source):
You can put this solution on YOUR website!
what you have to do is get the terms that are in the sqrt alone. So, first you have to is subtract the 3 and the x and bring them to the other side.
you get:
sqrt(x-8)=-x-3
then square both sides so you get
x-8=(-x-3)^2
then FOIL the right side
x-8=x^2+3x+3x+9
Add like terms and set it equal to zero.
x^2+5x+17=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B17+=+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=%285%29%5E2-4%2A1%2A17=-43.

The discriminant -43 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -43 is + or - sqrt%28+43%29+=+6.557438524302.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B17+%29