SOLUTION: solving a quadratic equation? 5y^2=-40

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Question 187448: solving a quadratic equation?

5y^2=-40
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5y%5E2=-40 Start with the given equation.


5y%5E2%2B40=0 Add 40 to both sides.



Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=5, b=0, and c=40


Let's use the quadratic formula to solve for y


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


y+=+%280+%2B-+sqrt%28+%280%29%5E2-4%285%29%2840%29+%29%29%2F%282%285%29%29 Plug in a=5, b=0, and c=40


y+=+%280+%2B-+sqrt%28+0-4%285%29%2840%29+%29%29%2F%282%285%29%29 Square 0 to get 0.


y+=+%280+%2B-+sqrt%28+0-800+%29%29%2F%282%285%29%29 Multiply 4%285%29%2840%29 to get 800


y+=+%280+%2B-+sqrt%28+-800+%29%29%2F%282%285%29%29 Subtract 800 from 0 to get -800


y+=+%280+%2B-+sqrt%28+-800+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


y+=+%280+%2B-+20i%2Asqrt%282%29%29%2F%2810%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


y+=+%280%29%2F%2810%29+%2B-+%2820i%2Asqrt%282%29%29%2F%2810%29 Break up the fraction.


y+=+0+%2B-+2%2Asqrt%282%29%2Ai Reduce.


y+=+2%2Asqrt%282%29%2Ai or y+=+-2%2Asqrt%282%29%2Ai Break up the expression.


So the answers are y+=+2%2Asqrt%282%29%2Ai or y+=+-2%2Asqrt%282%29%2Ai