SOLUTION: find the real common solution for -3x^2+18x-12

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Question 334996: find the real common solution for -3x^2+18x-12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the quadratic formula to get:

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 -3%2Ax%5E2%2B18%2Ax-12=0 ( notice a=-3, b=18, and c=-12)





x+=+%28-18+%2B-+sqrt%28+%2818%29%5E2-4%2A-3%2A-12+%29%29%2F%282%2A-3%29 Plug in a=-3, b=18, and c=-12




x+=+%28-18+%2B-+sqrt%28+324-4%2A-3%2A-12+%29%29%2F%282%2A-3%29 Square 18 to get 324




x+=+%28-18+%2B-+sqrt%28+324%2B-144+%29%29%2F%282%2A-3%29 Multiply -4%2A-12%2A-3 to get -144




x+=+%28-18+%2B-+sqrt%28+180+%29%29%2F%282%2A-3%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-18+%2B-+6%2Asqrt%285%29%29%2F%282%2A-3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-18+%2B-+6%2Asqrt%285%29%29%2F-6 Multiply 2 and -3 to get -6


So now the expression breaks down into two parts


x+=+%28-18+%2B+6%2Asqrt%285%29%29%2F-6 or x+=+%28-18+-+6%2Asqrt%285%29%29%2F-6



Now break up the fraction



x=-18%2F-6%2B6%2Asqrt%285%29%2F-6 or x=-18%2F-6-6%2Asqrt%285%29%2F-6



Simplify



x=3-sqrt%285%29 or x=3%2Bsqrt%285%29



So the solutions are:

x=3-sqrt%285%29 or x=3%2Bsqrt%285%29