SOLUTION: 3x^2 – 6x – 24 = 0

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Question 290301: 3x^2 – 6x – 24 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-6%2Ax-24=0 ( notice a=3, b=-6, and c=-24)





x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A3%2A-24+%29%29%2F%282%2A3%29 Plug in a=3, b=-6, and c=-24




x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A3%2A-24+%29%29%2F%282%2A3%29 Negate -6 to get 6




x+=+%286+%2B-+sqrt%28+36-4%2A3%2A-24+%29%29%2F%282%2A3%29 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because %28-6%29%5E2=-6%2A-6=36.)




x+=+%286+%2B-+sqrt%28+36%2B288+%29%29%2F%282%2A3%29 Multiply -4%2A-24%2A3 to get 288




x+=+%286+%2B-+sqrt%28+324+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%286+%2B-+18%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%286+%2B-+18%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%286+%2B+18%29%2F6 or x+=+%286+-+18%29%2F6


Lets look at the first part:


x=%286+%2B+18%29%2F6


x=24%2F6 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%286+-+18%29%2F6


x=-12%2F6 Subtract the terms in the numerator

x=-2 Divide


So another answer is

x=-2


So our solutions are:

x=4 or x=-2