SOLUTION: Need assistance please! I am asked to Solve a quadratic equation and show check of the potential answer's. Additionally, any excluded values should also be identified. a-4/a^

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Need assistance please! I am asked to Solve a quadratic equation and show check of the potential answer's. Additionally, any excluded values should also be identified. a-4/a^      Log On


   

Question 1126092: Need assistance please!
I am asked to Solve a quadratic equation and show check of the potential answer's. Additionally, any excluded values should also be identified.
a-4/a^2+5a -2/a+5=1/a^3+7a^2+10a
I worked through the problem and came up with a solution of a=-3.
Performing the check has me confused as I believe this is what will tell me if the values are excluded?
I did (-3+3)^2 which =0
I know 0 is an excluded value, but is the above the right approach or am I doing something wrong?
Thank you!
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28a-4%29%2F%28a%5E2%2B5a%29+-2%2F%28a%2B5%29=1%2F%28a%5E3%2B7a%5E2%2B10a+%29

%28a-4%29%2Fa%28a%2B5%29+-2%2F%28a%2B5%29=1%2Fa%28a%5E2%2B7a%2B10+%29

%28a-4%29%2Fa%28a%2B5%29+-2a%2Fa%28a%2B5%29=1%2Fa%28%28a+%2B+5%29+%28a+%2B+2%29+%29 => since denominator cannot be equal to zero, a%28%28a+%2B+5%29+%28a+%2B+2%29+%29 cannot be equal to zero too
so, a%28%28a+%2B+5%29+%28a+%2B+2%29+%29+=0 if a=0, a=-5, or+a=-2
therefore, we exclude these solutions

%28%28a-4%29-2a%29%2Fa%28a%2B5%29=1%2Fa%28%28a+%2B+5%29+%28a+%2B+2%29+%29




%28-a-4%29=1%2F+%28a+%2B+2%29

%28-a-4%29%28a+%2B+2%29=1

%28-a-4%29%28a+%2B+2%29-1=0

-a%5E2+-+6+a+-+9+=+0

-%28a+%2B+3%29%5E2+=+0

double solution is:
-%28a+%2B+3%29+=+0
-a-3=0
a=-3
so, your solution is highlight%28a=-3%29
and exclude solutions are a=-5, or+a=-2


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Need assistance please!
I am asked to Solve a quadratic equation and show check of the potential answer's. Additionally, any excluded values should also be identified.
a-4/a^2+5a -2/a+5=1/a^3+7a^2+10a
I worked through the problem and came up with a solution of a=-3.
Performing the check has me confused as I believe this is what will tell me if the values are excluded?
I did (-3+3)^2 which =0
I know 0 is an excluded value, but is the above the right approach or am I doing something wrong?
Thank you!
Your answer, - 3 is CORRECT!! Good work!



 ------------- Factoring denominators that can be factored

 ------------- Factoring denominator on right, further

We now see, based on the most previous equation that matrix%283%2C1%2C+a+%3C%3E0%2C+a+%3C%3E+-+5%2C+a+%3C%3E+-+2%29

Since the answer that you got - which is correct - is NONE of the above restricted values for "a", then we can say that it is indeed the solution.

The only thing I see here that's wrong is your calculation of %28a+%2B+3%29%5E2.

It's not part of any of the DENOMINATORS, so that's not how you check to see if your answer is CORRECT!