SOLUTION: 3x² - 9x + 7 = 0 be? How many solutions would that mean?

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Question 475456: 3x² - 9x + 7 = 0 be? How many solutions would that mean?

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%2B7=0 ( notice a=3, b=-9, and c=7)





x+=+%28--9+%2B-+sqrt%28+%28-9%29%5E2-4%2A3%2A7+%29%29%2F%282%2A3%29 Plug in a=3, b=-9, and c=7




x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%2A3%2A7+%29%29%2F%282%2A3%29 Negate -9 to get 9




x+=+%289+%2B-+sqrt%28+81-4%2A3%2A7+%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%2B-84+%29%29%2F%282%2A3%29 Multiply -4%2A7%2A3 to get -84




x+=+%289+%2B-+sqrt%28+-3+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%289+%2B-+i%2Asqrt%283%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-+i%2Asqrt%283%29%29%2F%286%29 Multiply 2 and 3 to get 6




After simplifying, the quadratic has roots of


x=3%2F2%2Bsqrt%283%29%2F6%2Ai or x=3%2F2-sqrt%283%29%2F6%2Ai