SOLUTION: What is "x(squared)+6x+15=0" in a+bi form?

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Question 568299: What is "x(squared)+6x+15=0" in a+bi form?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B15=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B15 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=15


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%2815%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=15


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%2815%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-60+%29%29%2F%282%281%29%29 Multiply 4%281%29%2815%29 to get 60


x+=+%28-6+%2B-+sqrt%28+-24+%29%29%2F%282%281%29%29 Subtract 60 from 36 to get -24


x+=+%28-6+%2B-+sqrt%28+-24+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+2i%2Asqrt%286%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-+%282i%2Asqrt%286%29%29%2F%282%29 Break up the fraction.


x+=+-3+%2B-+sqrt%286%29%2Ai Reduce.


x+=+-3%2Bsqrt%286%29%2Ai or x+=+-3-sqrt%286%29%2Ai Break up the expression.


So the solutions are x+=+-3%2Bsqrt%286%29%2Ai or x+=+-3-sqrt%286%29%2Ai
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