SOLUTION: 2=-9x^2 - x

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Question 171090: 2=-9x^2 - x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


2%2B9x%5E2%2B1x=0 Get all terms to the left side.


9x%5E2%2Bx%2B2=0 Rearrange the terms.


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


x+=+%28-1+%2B-+sqrt%28+1-4%289%29%282%29+%29%29%2F%282%289%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1-72+%29%29%2F%282%289%29%29 Multiply 4%289%29%282%29 to get 72


x+=+%28-1+%2B-+sqrt%28+-71+%29%29%2F%282%289%29%29 Subtract 72 from 1 to get -71


x+=+%28-1+%2B-+sqrt%28+-71+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%28-1+%2B-+i%2Asqrt%2871%29%29%2F%2818%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-1%2Bi%2Asqrt%2871%29%29%2F%2818%29 or x+=+%28-1-i%2Asqrt%2871%29%29%2F%2818%29 Break up the expression.


So the answers are x+=+%28-1%2Bi%2Asqrt%2871%29%29%2F%2818%29 or x+=+%28-1-i%2Asqrt%2871%29%29%2F%2818%29


which approximate to x=-0.556%2B0.468%2Ai or x=-0.5556-0.468%2Ai