SOLUTION: Solve for x 3x^2=2x+21

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Question 416794: Solve for x
3x^2=2x+21
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2=2x%2B21 Start with the given equation.


3x%5E2-2x-21=0 Get every term to the left side.


Notice that the quadratic 3x%5E2-2x-21 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-2, and C=-21


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%28-21%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-2, and C=-21


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%28-21%29+%29%29%2F%282%283%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%283%29%28-21%29+%29%29%2F%282%283%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--252+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-21%29 to get -252


x+=+%282+%2B-+sqrt%28+4%2B252+%29%29%2F%282%283%29%29 Rewrite sqrt%284--252%29 as sqrt%284%2B252%29


x+=+%282+%2B-+sqrt%28+256+%29%29%2F%282%283%29%29 Add 4 to 252 to get 256


x+=+%282+%2B-+sqrt%28+256+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%282+%2B-+16%29%2F%286%29 Take the square root of 256 to get 16.


x+=+%282+%2B+16%29%2F%286%29 or x+=+%282+-+16%29%2F%286%29 Break up the expression.


x+=+%2818%29%2F%286%29 or x+=++%28-14%29%2F%286%29 Combine like terms.


x+=+3 or x+=+-7%2F3 Simplify.


So the solutions are x+=+3 or x+=+-7%2F3

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