SOLUTION: Help! Determine the number of real solutions of -x^2 -6x - 12=0 Use the quadratic formula to find the exact values of the real solutions, if they exist. Give the solution Se

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Question 874285: Help!
Determine the number of real solutions of -x^2 -6x - 12=0
Use the quadratic formula to find the exact values of the real solutions, if they exist. Give the solution Set.
Use a calculator to find approximations for the answers. Round your answers to the nearest thousandth.
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 -x%5E2-6%2Ax-12=0 ( notice a=-1, b=-6, and c=-12)





x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A-1%2A-12+%29%29%2F%282%2A-1%29 Plug in a=-1, b=-6, and c=-12




x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A-1%2A-12+%29%29%2F%282%2A-1%29 Negate -6 to get 6




x+=+%286+%2B-+sqrt%28+36-4%2A-1%2A-12+%29%29%2F%282%2A-1%29 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because %28-6%29%5E2=-6%2A-6=36.)




x+=+%286+%2B-+sqrt%28+36%2B-48+%29%29%2F%282%2A-1%29 Multiply -4%2A-12%2A-1 to get -48




x+=+%286+%2B-+sqrt%28+-12+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)




x+=+%286+%2B-+2%2Ai%2Asqrt%283%29%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%286+%2B-+2%2Ai%2Asqrt%283%29%29%2F%28-2%29 Multiply 2 and -1 to get -2




After simplifying, the quadratic has roots of


x=-3-sqrt%283%29i or x=-3%2Bsqrt%283%29i