SOLUTION: 12. Solve. Find the exact solution(s). Show work. 5x^2 + 8x + 5 = 0

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Question 150018: 12. Solve. Find the exact solution(s). Show work. 5x^2 + 8x + 5 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From the equation 5x%5E2+%2B+8x+%2B+5+=+0, we can see that a=5, b=8, and c=5


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


x+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%285%29%285%29+%29%29%2F%282%285%29%29 Plug in a=5, b=8, and c=5


x+=+%28-8+%2B-+sqrt%28+64-4%285%29%285%29+%29%29%2F%282%285%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64-100+%29%29%2F%282%285%29%29 Multiply 4%285%29%285%29 to get 100


x+=+%28-8+%2B-+sqrt%28+-36+%29%29%2F%282%285%29%29 Subtract 100 from 64 to get -36


x+=+%28-8+%2B-+sqrt%28+-36+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%28-8+%2B-+6%2Ai%29%2F%2810%29 Take the square root of -36 to get 6%2Ai.


x+=+%28-8+%2B+6%2Ai%29%2F%2810%29 or x+=+%28-8+-+6%2Ai%29%2F%2810%29 Break up the expression.


x+=+%28-8%29%2F%2810%29+%2B+%286%2Ai%29%2F%2810%29 or x+=++%28-8%29%2F%2810%29+-+%286%2Ai%29%2F%2810%29 Break up the fraction for each case.


x+=+-4%2F5%2B%283%2F5%29%2Ai or x+=+-4%2F5-%283%2F5%29%2Ai Reduce.


So the answers are x+=+-4%2F5%2B%283%2F5%29%2Ai or x+=+-4%2F5-%283%2F5%29%2Ai