SOLUTION: please help me solve this equation: x^2+6x+41=0

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Question 540200: please help me solve this equation: x^2+6x+41=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B41=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B41 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=41


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%2841%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=41


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%2841%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-164+%29%29%2F%282%281%29%29 Multiply 4%281%29%2841%29 to get 164


x+=+%28-6+%2B-+sqrt%28+-128+%29%29%2F%282%281%29%29 Subtract 164 from 36 to get -128


x+=+%28-6+%2B-+sqrt%28+-128+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+8i%2Asqrt%282%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%29%2F%282%29+%2B-+%288i%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+-3+%2B-+4%2Asqrt%282%29%2Ai Reduce.


x+=+-3%2B4%2Asqrt%282%29%2Ai or x+=+-3-4%2Asqrt%282%29%2Ai Break up the expression.


So the solutions are x+=+-3%2B4%2Asqrt%282%29%2Ai or x+=+-3-4%2Asqrt%282%29%2Ai


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim