SOLUTION: 18x^2 +9x + 1=0 answer: x= -1/3 or -1/6 need a full break down of how my text book got this answer

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Question 184810: 18x^2 +9x + 1=0

answer: x= -1/3 or -1/6

need a full break down of how my text book got this answer
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

18x%5E2%2B9x%2B1=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=18, 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-%289%29+%2B-+sqrt%28+%289%29%5E2-4%2818%29%281%29+%29%29%2F%282%2818%29%29 Plug in a=18, b=9, and c=1


x+=+%28-9+%2B-+sqrt%28+81-4%2818%29%281%29+%29%29%2F%282%2818%29%29 Square 9 to get 81.


x+=+%28-9+%2B-+sqrt%28+81-72+%29%29%2F%282%2818%29%29 Multiply 4%2818%29%281%29 to get 72


x+=+%28-9+%2B-+sqrt%28+9+%29%29%2F%282%2818%29%29 Subtract 72 from 81 to get 9


x+=+%28-9+%2B-+sqrt%28+9+%29%29%2F%2836%29 Multiply 2 and 18 to get 36.


x+=+%28-9+%2B-+3%29%2F%2836%29 Take the square root of 9 to get 3.


x+=+%28-9+%2B+3%29%2F%2836%29 or x+=+%28-9+-+3%29%2F%2836%29 Break up the expression.


x+=+%28-6%29%2F%2836%29 or x+=++%28-12%29%2F%2836%29 Combine like terms.


x+=+-1%2F6 or x+=+-1%2F3 Simplify.


So the answers are x+=+-1%2F6 or x+=+-1%2F3

Note: the order of the solutions does not matter