SOLUTION: I have to completely factor 5x^2-12=-17x. Can someone help me with this problem.

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Question 112065: I have to completely factor 5x^2-12=-17x. Can someone help me with this problem.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation


Add 17x to both sides


Rearrange the terms


Let's use the quadratic formula to solve for x:


Starting with the general quadratic



the general solution using the quadratic equation is:





So lets solve ( notice , , and )




Plug in a=5, b=17, and c=-12



Square 17 to get 289



Multiply to get



Combine like terms in the radicand (everything under the square root)



Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



Multiply 2 and 5 to get 10

So now the expression breaks down into two parts

or

Lets look at the first part:



Add the terms in the numerator
Divide

So one answer is




Now lets look at the second part:



Subtract the terms in the numerator
Divide

So another answer is


So our solutions are:
or

Notice when we graph , we get:



and we can see that the roots are and . This verifies our answer

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