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) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2-12=-17x Start with the given equation


5x%5E2-12%2B17x=0 Add 17x to both sides


5x%5E2%2B17x-12=0 Rearrange the terms


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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve 5%2Ax%5E2%2B17%2Ax-12=0 ( notice a=5, b=17, and c=-12)




x+=+%28-17+%2B-+sqrt%28+%2817%29%5E2-4%2A5%2A-12+%29%29%2F%282%2A5%29 Plug in a=5, b=17, and c=-12



x+=+%28-17+%2B-+sqrt%28+289-4%2A5%2A-12+%29%29%2F%282%2A5%29 Square 17 to get 289



x+=+%28-17+%2B-+sqrt%28+289%2B240+%29%29%2F%282%2A5%29 Multiply -4%2A-12%2A5 to get 240



x+=+%28-17+%2B-+sqrt%28+529+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-17+%2B-+23%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-17+%2B-+23%29%2F10 Multiply 2 and 5 to get 10

So now the expression breaks down into two parts

x+=+%28-17+%2B+23%29%2F10 or x+=+%28-17+-+23%29%2F10

Lets look at the first part:

x=%28-17+%2B+23%29%2F10

x=6%2F10 Add the terms in the numerator
x=3%2F5 Divide

So one answer is
x=3%2F5



Now lets look at the second part:

x=%28-17+-+23%29%2F10

x=-40%2F10 Subtract the terms in the numerator
x=-4 Divide

So another answer is
x=-4

So our solutions are:
x=3%2F5 or x=-4

Notice when we graph 5%2Ax%5E2%2B17%2Ax-12, we get:

+graph%28+500%2C+500%2C+-14%2C+13%2C+-14%2C+13%2C5%2Ax%5E2%2B17%2Ax%2B-12%29+

and we can see that the roots are x=3%2F5 and x=-4. This verifies our answer