SOLUTION: f(x)=-6x^2+6x+12. How do i solve for x? thanks!

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Question 604124: f(x)=-6x^2+6x+12. How do i solve for x?
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the quadratic formula

Solved by pluggable solver: Quadratic Formula
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 -6%2Ax%5E2%2B6%2Ax%2B12=0 ( notice a=-6, b=6, and c=12)





x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A-6%2A12+%29%29%2F%282%2A-6%29 Plug in a=-6, b=6, and c=12




x+=+%28-6+%2B-+sqrt%28+36-4%2A-6%2A12+%29%29%2F%282%2A-6%29 Square 6 to get 36




x+=+%28-6+%2B-+sqrt%28+36%2B288+%29%29%2F%282%2A-6%29 Multiply -4%2A12%2A-6 to get 288




x+=+%28-6+%2B-+sqrt%28+324+%29%29%2F%282%2A-6%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-6+%2B-+18%29%2F%282%2A-6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-6+%2B-+18%29%2F-12 Multiply 2 and -6 to get -12


So now the expression breaks down into two parts


x+=+%28-6+%2B+18%29%2F-12 or x+=+%28-6+-+18%29%2F-12


Lets look at the first part:


x=%28-6+%2B+18%29%2F-12


x=12%2F-12 Add the terms in the numerator

x=-1 Divide


So one answer is

x=-1




Now lets look at the second part:


x=%28-6+-+18%29%2F-12


x=-24%2F-12 Subtract the terms in the numerator

x=2 Divide


So another answer is

x=2


So our solutions are:

x=-1 or x=2