SOLUTION: How to find the root(s) of 80-x^2=0 And How to simplify 4x^3+6x^2-14x/2x Thank you!

Question 708305: How to find the root(s) of 80-x^2=0
And
How to simplify 4x^3+6x^2-14x/2x
Thank you!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Any quadratic equation can be solved using the Quadratic Formula. Or, since there is no x-term (just x-squared), we can solve this more simply. Adding to each side we get:

Now we find the square root of each side. Since there both positive and negative square roots we end up with two equations:
or
All that's left is to simplify the square root. Since 80 = 16*5 and since 16 is a perfect square, these square roots will simplify:

Substituting the simplified square roots into our solutions we get:
or

In the future, put parentheses around multiple-term numerators and denominators. Without the parentheses what you posted meant:

But I strongly suspect that the actual fraction is:

Believe it or not, simplifying/reducing fractions is the same as it has always been. Any factors that are common to both the numerator and denominator can be canceled. What has changed since the "good old days" of reducing fractions like 10/20 is that it is harder to find the factors.

So to see if the fraction will simplify/reduce is to find the factors. And when factoring we always start with the greatest common factor, GCF. The GCF in the numerator is 2x. The GCF in the denominator is just 1. Factoring the GCF's out we get:

As we can see, we do have a factor in common, 2x, which we can cancel:

leaving:

which simplifies to:

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