You can put this solution on YOUR website! There a several ways to solve this. The easiest is to use the quadratic equation, however I suspect, given the results I get from the quadratic equation, that you are actually required to factor the problem, so, how do you do this?
First, notice that you result will have to have the form
.
The goal is to find the values for a and b. To do this notice that according to the equation,:
a + 2b = 9 and
ab = -5
There are four ways to make ab = -5:
a b ab
5 -1 -5
-5 1 -5
1 -5 -5
-1 5 -5
One of these combinations must also give us 9, so let's consider what happens with these combinations when we apply them to a + 2b:
a b ab
5 -1 3
-5 1 -3
1 -5 -9
-1 5 9
The last combination gives us the value we want. This means a = -1 and b = 5 works. So the factorization of is .
This expression is zero when 2x - 1 = 0 or when x + 5 = 0. So the values of x that make the expression equal to zero are x = 1/2 and x = -5.
You can check this by replacing these values in the expression.
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