SOLUTION: solve using the quadratic formula 9x -2 = 3x^2

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Question 200964This question is from textbook Beginning Algebra
: solve using the quadratic formula
9x -2 = 3x^2 This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9x+-2+=+3x%5E2 Start with the given equation.


0+=+3x%5E2-9x%2B2 Get everything to one side


Notice that the quadratic 3x%5E2-9x%2B2 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-9, 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-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%283%29%282%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-9, and C=2


x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%283%29%282%29+%29%29%2F%282%283%29%29 Negate -9 to get 9.


x+=+%289+%2B-+sqrt%28+81-4%283%29%282%29+%29%29%2F%282%283%29%29 Square -9 to get 81.


x+=+%289+%2B-+sqrt%28+81-24+%29%29%2F%282%283%29%29 Multiply 4%283%29%282%29 to get 24


x+=+%289+%2B-+sqrt%28+57+%29%29%2F%282%283%29%29 Subtract 24 from 81 to get 57


x+=+%289+%2B-+sqrt%28+57+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%289%2Bsqrt%2857%29%29%2F%286%29 or x+=+%289-sqrt%2857%29%29%2F%286%29 Break up the expression.


So the solutions are x+=+%289%2Bsqrt%2857%29%29%2F%286%29 or x+=+%289-sqrt%2857%29%29%2F%286%29


which approximate to x=2.758 or x=0.242