SOLUTION: Solve using the Quadratic Formula: x^2 + 4x + 6 = 0

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Question 536583: Solve using the Quadratic Formula:
x^2 + 4x + 6 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B4x%2B6=0 Start with the given equation.


Notice that the quadratic x%5E2%2B4x%2B6 is in the form of Ax%5E2%2BBx%2BC where A=1, B=4, and C=6


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-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Plug in A=1, B=4, and C=6


x+=+%28-4+%2B-+sqrt%28+16-4%281%29%286%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16-24+%29%29%2F%282%281%29%29 Multiply 4%281%29%286%29 to get 24


x+=+%28-4+%2B-+sqrt%28+-8+%29%29%2F%282%281%29%29 Subtract 24 from 16 to get -8


x+=+%28-4+%2B-+sqrt%28+-8+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-4+%2B-+2i%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+=+%28-4%29%2F%282%29+%2B-+%282i%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+-2+%2B-+sqrt%282%29%2Ai Reduce.


x+=+-2%2Bsqrt%282%29%2Ai or x+=+-2-sqrt%282%29%2Ai Break up the expression.


So the solutions are x+=+-2%2Bsqrt%282%29%2Ai or x+=+-2-sqrt%282%29%2Ai


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Jim