SOLUTION: 16. What are the roots of the equation 3x2 − 9x − 5 = 0? (Points : 5)

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Question 463852: 16. What are the roots of the equation 3x2 − 9x − 5 = 0?
(Points : 5)
Answer by MathLover1(20849) 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%5E2-9%2Ax-5=0 ( notice a=3, b=-9, and c=-5)





x+=+%28--9+%2B-+sqrt%28+%28-9%29%5E2-4%2A3%2A-5+%29%29%2F%282%2A3%29 Plug in a=3, b=-9, and c=-5




x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%2A3%2A-5+%29%29%2F%282%2A3%29 Negate -9 to get 9




x+=+%289+%2B-+sqrt%28+81-4%2A3%2A-5+%29%29%2F%282%2A3%29 Square -9 to get 81 (note: remember when you square -9, you must square the negative as well. This is because %28-9%29%5E2=-9%2A-9=81.)




x+=+%289+%2B-+sqrt%28+81%2B60+%29%29%2F%282%2A3%29 Multiply -4%2A-5%2A3 to get 60




x+=+%289+%2B-+sqrt%28+141+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%289+%2B-+sqrt%28141%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%289+%2B-+sqrt%28141%29%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%289+%2B+sqrt%28141%29%29%2F6 or x+=+%289+-+sqrt%28141%29%29%2F6



Now break up the fraction



x=%2B9%2F6%2Bsqrt%28141%29%2F6 or x=%2B9%2F6-sqrt%28141%29%2F6



Simplify



x=3%2F2%2Bsqrt%28141%29%2F6 or x=3%2F2-sqrt%28141%29%2F6



So the solutions are:

x=3%2F2%2Bsqrt%28141%29%2F6 or x=3%2F2-sqrt%28141%29%2F6




x=3%2F2%2B%2811.87%29%2F6 or x=3%2F2-%2811.87%29%2F6
x=1.5%2B1.978 or x=1.5-1.978
x=3.478 or x=-0.478