SOLUTION: Use the quadratic formula to solve for x 6x^2-9x+1=0 if more than 1 solution separate with a comma

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Question 294259: Use the quadratic formula to solve for x
6x^2-9x+1=0
if more than 1 solution separate with a comma
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E2-9x%2B1=0 Start with the given equation.


Notice that the quadratic 6x%5E2-9x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=6, B=-9, 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-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%286%29%281%29+%29%29%2F%282%286%29%29 Plug in A=6, B=-9, and C=1


x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%286%29%281%29+%29%29%2F%282%286%29%29 Negate -9 to get 9.


x+=+%289+%2B-+sqrt%28+81-4%286%29%281%29+%29%29%2F%282%286%29%29 Square -9 to get 81.


x+=+%289+%2B-+sqrt%28+81-24+%29%29%2F%282%286%29%29 Multiply 4%286%29%281%29 to get 24


x+=+%289+%2B-+sqrt%28+57+%29%29%2F%282%286%29%29 Subtract 24 from 81 to get 57


x+=+%289+%2B-+sqrt%28+57+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%289%2Bsqrt%2857%29%29%2F%2812%29 or x+=+%289-sqrt%2857%29%29%2F%2812%29 Break up the expression.


So the solutions are x+=+%289%2Bsqrt%2857%29%29%2F%2812%29 or x+=+%289-sqrt%2857%29%29%2F%2812%29