SOLUTION: solve the equation with the quadratic formula: 9m^2=-2

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Question 201640: solve the equation with the quadratic formula:
9m^2=-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


9m%5E2%2B2=0 Get all terms to the left side.


Notice that the quadratic 9m%5E2%2B2 is in the form of Am%5E2%2BBm%2BC where A=9, B=0, and C=2


Let's use the quadratic formula to solve for "m":


m+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


m+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%289%29%282%29+%29%29%2F%282%289%29%29 Plug in A=9, B=0, and C=2


m+=+%280+%2B-+sqrt%28+0-4%289%29%282%29+%29%29%2F%282%289%29%29 Square 0 to get 0.


m+=+%280+%2B-+sqrt%28+0-72+%29%29%2F%282%289%29%29 Multiply 4%289%29%282%29 to get 72


m+=+%280+%2B-+sqrt%28+-72+%29%29%2F%282%289%29%29 Subtract 72 from 0 to get -72


m+=+%280+%2B-+sqrt%28+-72+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


m+=+%280+%2B-+6i%2Asqrt%282%29%29%2F%2818%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


m+=+%286i%2Asqrt%282%29%29%2F%2818%29 or m+=+-%286i%2Asqrt%282%29%29%2F%2818%29 Break up the expression.


m+=+%281%2F3%29%2Ai%2Asqrt%282%29 or m+=+-%281%2F3%29%2Ai%2Asqrt%282%29 Reduce


So the solutions are m+=+%281%2F3%29%2Ai%2Asqrt%282%29 or m+=+-%281%2F3%29%2Ai%2Asqrt%282%29