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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