SOLUTION: Hi, I'm studying for a test, and I need help with this problem. Find all real solutions (a,b are positive constants) {{{10a^2x^2-2abx-36b^2=0}}} I know that it needs to b

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, I'm studying for a test, and I need help with this problem. Find all real solutions (a,b are positive constants) {{{10a^2x^2-2abx-36b^2=0}}} I know that it needs to b      Log On


   

Question 70598This question is from textbook College Algebra Essentials
: Hi, I'm studying for a test, and I need help with this problem.
Find all real solutions (a,b are positive constants)
10a%5E2x%5E2-2abx-36b%5E2=0
I know that it needs to be solved by factoring, completing the square, or the quadratic formula, but don't know where to start.
Thanks!
This question is from textbook College Algebra Essentials

Found 2 solutions by Earlsdon, checkley75:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
10a%5Ex%5E2-2abx-36b%5E2+=+0 This can be factored.
2%285ax%2B9b%29%28ax-2b%29+=+0 Applying the zero product principle:
5ax%2B9b+=+0 and/or ax-2b+=+0
If 5ax%2B9b+=+0 then 5ax+=+-9b so x+=+-%289b%29%2F5a
If ax-2b+=+0 then ax+=+2b so x+=+2b%2Fa

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
FIRST WE FACTOR OUT THE COMMON FACTOR (2)
2(5A^2X^2-ABX-18B^2) NOW FACTOR THE QUADRATIC EQUATION THUS
2(5AX+9B)(AX-2B)