SOLUTION: Please help with this. Find all solutions of the equation. check your solutions in the original equation. x + the square root of 31-9x = 5 31-9x is under the square root

Algebra ->  Equations -> SOLUTION: Please help with this. Find all solutions of the equation. check your solutions in the original equation. x + the square root of 31-9x = 5 31-9x is under the square root      Log On


   

Question 44416This question is from textbook College Algebra
: Please help with this.
Find all solutions of the equation. check your solutions in the original equation.
x + the square root of 31-9x = 5

31-9x is under the square root symbol
thank you This question is from textbook College Algebra

Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+sqrt%2831-9x%29+=+5
Rearrang so the square root is the only term on the right hand side:
5-xsqrt%2831-9x%29
Now square both sides:
%285-x%29%5E2=31-9x
Use FOIL to expand the left hand side:
25-10x%2Bx%5E2=31-9x
Rearrange to give a quadratic expression with zero on the right hand side:
x%5E2-10x%2B9x%2B25-31=0
x%5E2-x-6=0
Factorise:
%28x%2B2%29%28x-3%29=0
So the solutions are x=-2 or x=3.
I have plotted the curve y=x+%2B+sqrt%2831-9x%29 and the line y=5 Below. Note thet the solutions occur when the red line intersects the green line, when x=-2 and when x=3. This proves The solutions are accurate.
+graph%28+300%2C+200%2C+-3%2C+3.4%2C+-1%2C+6%2C+x+%2B+sqrt%2831-9x%29%2C+5%29+
I hope this helps.
I am currently constructing my own homework help website, and would greatly appreciate any feedback on the help you recieved to my email address: adam.chapman@student.manchester.ac.uk
Adam