SOLUTION: solve the equation for x and express the roots in simplest a+ bi form: 3x^2=2x-1

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Question 585882: solve the equation for x and express the roots in simplest a+ bi form: 3x^2=2x-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2=2x-1 Start with the given equation.


3x%5E2-2x%2B1=0 Get every term to the left side.


Notice that the quadratic 3x%5E2-2x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-2, and C=1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%281%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-2, and C=1


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%281%29+%29%29%2F%282%283%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%283%29%281%29+%29%29%2F%282%283%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4-12+%29%29%2F%282%283%29%29 Multiply 4%283%29%281%29 to get 12


x+=+%282+%2B-+sqrt%28+-8+%29%29%2F%282%283%29%29 Subtract 12 from 4 to get -8


x+=+%282+%2B-+sqrt%28+-8+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


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


x+=+%282%2B2i%2Asqrt%282%29%29%2F%286%29 or x+=+%282-2i%2Asqrt%282%29%29%2F%286%29 Break up the expression.


x+=+%281%2Bi%2Asqrt%282%29%29%2F%283%29 or x+=+%281-i%2Asqrt%282%29%29%2F%283%29 Reduce


x+=+1%2F3+%2B+expr%28sqrt%282%29%2F3%29i or x+=+1%2F3+-+expr%28sqrt%282%29%2F3%29i Break up the fraction and rearrange terms.


So the solutions are x+=+1%2F3+%2B+expr%28sqrt%282%29%2F3%29i or x+=+1%2F3+-+expr%28sqrt%282%29%2F3%29i

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