SOLUTION: find all real and/or imaginary solutions: 16xSQUARED + 48x + 40 = 0

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Question 112286: find all real and/or imaginary solutions: 16xSQUARED + 48x + 40 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 16%2Ax%5E2%2B48%2Ax%2B40=0 ( notice a=16, b=48, and c=40)





x+=+%28-48+%2B-+sqrt%28+%2848%29%5E2-4%2A16%2A40+%29%29%2F%282%2A16%29 Plug in a=16, b=48, and c=40




x+=+%28-48+%2B-+sqrt%28+2304-4%2A16%2A40+%29%29%2F%282%2A16%29 Square 48 to get 2304




x+=+%28-48+%2B-+sqrt%28+2304%2B-2560+%29%29%2F%282%2A16%29 Multiply -4%2A40%2A16 to get -2560




x+=+%28-48+%2B-+sqrt%28+-256+%29%29%2F%282%2A16%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-48+%2B-+16%2Ai%29%2F%282%2A16%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-48+%2B-+16%2Ai%29%2F%2832%29 Multiply 2 and 16 to get 32




After simplifying, the quadratic has roots of


x=-3%2F2%2B1%2F2%2Ai or x=-3%2F2-1%2F2%2Ai