SOLUTION: Hello I need to solve: {{{ 3x^2-4x=5 }}} and {{{ (-(x+2)^2(x-1))/(x(x-3)) }}} greater than or equal to 0. I know these are quadratic equations and I may be able to solve by co

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello I need to solve: {{{ 3x^2-4x=5 }}} and {{{ (-(x+2)^2(x-1))/(x(x-3)) }}} greater than or equal to 0. I know these are quadratic equations and I may be able to solve by co      Log On


   

Question 892670: Hello
I need to solve:
+3x%5E2-4x=5+
and
+%28-%28x%2B2%29%5E2%28x-1%29%29%2F%28x%28x-3%29%29+ greater than or equal to 0.
I know these are quadratic equations and I may be able to solve by completing
square or applying it into the quadratic equation, but I'm having a little
trouble solving it that way.
Thanks
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The first quadratic equation is no big deal - use the general solution if you cannot factorize for solving.

The rational equation is a bigger deal than your quadratic equation earlier. The denominator is mostly unimportant. The numerator must be zero for the expreesion (and equation) to equal zero.

-%28x%2B2%29%5E2%28x-1%29=0
%28x%2B2%29%5E2%2A%28x-1%29=0, and is already in factored form. Use the zero-product property. One or the other of the binomial factors must be zero. No complications occur with the denominator because numerator and denominator do not share any of the same factors.

Either x+2=0 and therefore x=-2;
Or
x-1=0 and therefore x=1.
ANSWER: x = -2 OR 1.

YOU WANTED GREATER OR EQUAL TO ZERO.
In this case, the zeros found, and the undefined value of x where denominator would be zero are the critical values of x around which to check. These critical values of x are: -2, 1, 3. Those form these four intervals of x:

-infinity%3C=x%3C=-2
'
-2%3C=x%3C=1
'
1%3C=x%3C3
'
3%3Cx%3C=infinity

Pick any value within each interval to check the truth or falsity of the rational inequality. That task is for you to do and finish. A result which makes the inequality true means that interval is a solution; a result which makes the inequality false means that interval is not part of the solution.