SOLUTION: sovle over the complex numbers 5k squared = 3k + 2

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Question 176922: sovle over the complex numbers
5k squared = 3k + 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5k%5E2=3k%2B2 Start with the given equation.


5k%5E2-3k-2=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ak%5E2%2Bbk%2Bc where a=5, b=-3, and c=-2


Let's use the quadratic formula to solve for k


k+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


k+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%28-2%29+%29%29%2F%282%285%29%29 Plug in a=5, b=-3, and c=-2


k+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%28-2%29+%29%29%2F%282%285%29%29 Negate -3 to get 3.


k+=+%283+%2B-+sqrt%28+9-4%285%29%28-2%29+%29%29%2F%282%285%29%29 Square -3 to get 9.


k+=+%283+%2B-+sqrt%28+9--40+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-2%29 to get -40


k+=+%283+%2B-+sqrt%28+9%2B40+%29%29%2F%282%285%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


k+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%285%29%29 Add 9 to 40 to get 49


k+=+%283+%2B-+sqrt%28+49+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


k+=+%283+%2B-+7%29%2F%2810%29 Take the square root of 49 to get 7.


k+=+%283+%2B+7%29%2F%2810%29 or k+=+%283+-+7%29%2F%2810%29 Break up the expression.


k+=+%2810%29%2F%2810%29 or k+=++%28-4%29%2F%2810%29 Combine like terms.


k+=+1 or k+=+-2%2F5 Simplify.


So the answers are k+=+1 or k+=+-2%2F5