SOLUTION: x^2+6x+34=0

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Question 591815: x^2+6x+34=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B34=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B34 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=34


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%281%29%2834%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=34


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%2834%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-136+%29%29%2F%282%281%29%29 Multiply 4%281%29%2834%29 to get 136


x+=+%28-6+%2B-+sqrt%28+-100+%29%29%2F%282%281%29%29 Subtract 136 from 36 to get -100


x+=+%28-6+%2B-+sqrt%28+-100+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+10%2Ai%29%2F%282%29 Take the square root of -100 to get 10%2Ai.


x+=+%28-6+%2B+10%2Ai%29%2F%282%29 or x+=+%28-6+-+10%2Ai%29%2F%282%29 Break up the expression.


x+=+%28-6%29%2F%282%29+%2B+%2810%2Ai%29%2F%282%29 or x+=++%28-6%29%2F%282%29+-+%2810%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+-3%2B5%2Ai or x+=++-3-5%2Ai Reduce.


So the solutions are x+=+-3%2B5%2Ai or x+=+-3-5%2Ai