SOLUTION: 3x^2=2(x+1)

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Question 318434: 3x^2=2(x+1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2=2%28x%2B1%29 Start with the given equation.


3x%5E2=2x%2B2 Distribute.


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


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


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%28-2%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-2, and C=-2


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


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


x+=+%282+%2B-+sqrt%28+4--24+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-2%29 to get -24


x+=+%282+%2B-+sqrt%28+4%2B24+%29%29%2F%282%283%29%29 Rewrite sqrt%284--24%29 as sqrt%284%2B24%29


x+=+%282+%2B-+sqrt%28+28+%29%29%2F%282%283%29%29 Add 4 to 24 to get 28


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


x+=+%282+%2B-+2%2Asqrt%287%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%2B2%2Asqrt%287%29%29%2F%286%29 or x+=+%282-2%2Asqrt%287%29%29%2F%286%29 Break up the expression.


x+=+%281%2Bsqrt%287%29%29%2F%283%29 or x+=+%281-sqrt%287%29%29%2F%283%29 Reduce.


So the solutions are x+=+%281%2Bsqrt%287%29%29%2F%283%29 or x+=+%281-sqrt%287%29%29%2F%283%29