SOLUTION: 3xsquared + 4x =-2

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Question 211226: 3xsquared + 4x =-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B4x=-2 Start with the given equation.


3x%5E2%2B4x%2B2=0 Add 2 to both sides.


Notice that the quadratic 3x%5E2%2B4x%2B2 is in the form of Ax%5E2%2BBx%2BC where A=3, B=4, and C=2


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%283%29%282%29+%29%29%2F%282%283%29%29 Plug in A=3, B=4, and C=2


x+=+%28-4+%2B-+sqrt%28+16-4%283%29%282%29+%29%29%2F%282%283%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16-24+%29%29%2F%282%283%29%29 Multiply 4%283%29%282%29 to get 24


x+=+%28-4+%2B-+sqrt%28+-8+%29%29%2F%282%283%29%29 Subtract 24 from 16 to get -8


x+=+%28-4+%2B-+sqrt%28+-8+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-4+%2B-+2i%2Asqrt%282%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-4%2B2i%2Asqrt%282%29%29%2F%286%29 or x+=+%28-4-2i%2Asqrt%282%29%29%2F%286%29 Break up the expression.


x+=+%28-2%2Bi%2Asqrt%282%29%29%2F%283%29 or x+=+%28-2-i%2Asqrt%282%29%29%2F%283%29 Reduce.


So the solutions are x+=+%28-2%2Bi%2Asqrt%282%29%29%2F%283%29 or x+=+%28-2-i%2Asqrt%282%29%29%2F%283%29