SOLUTION: Find the solution: 2x2 + 6x + 5 = 0.

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Question 186440: Find the solution: 2x2 + 6x + 5 = 0.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B6x%2B5=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=6, and c=5


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-%286%29+%2B-+sqrt%28+%286%29%5E2-4%282%29%285%29+%29%29%2F%282%282%29%29 Plug in a=2, b=6, and c=5


x+=+%28-6+%2B-+sqrt%28+36+-+4%282%29%285%29+%29%29%2F%282%282%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36+-+40%29%29%2F%282%282%29%29 Multiply 4%282%29%285%29 to get 40


x+=+%28-6+%2B-+sqrt%28-4%29%29%2F%282%282%29%29 Subtract 40 from 36 to get -4


x+=+%28-6+%2B-+sqrt%28+-4+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-6+%2B-+2%2Ai%29%2F%284%29 Take the square root of -4 to get 2%2Ai.


x+=+%28-6+%2B+2%2Ai%29%2F%284%29 or x+=+%28-6+-+2%2Ai%29%2F%284%29 Break up the expression.


x+=+%28-6%29%2F%284%29+%2B+%282%2Ai%29%2F%284%29 or x+=++%28-6%29%2F%284%29+-+%282%2Ai%29%2F%284%29 Break up the fraction for each case.


x+=+-3%2F2%2B%281%2F2%29%2Ai or x+=++-3%2F2-%281%2F2%29%2Ai Reduce.


So the answers are x+=+-3%2F2%2B%281%2F2%29%2Ai or x+=++-3%2F2-%281%2F2%29%2Ai