SOLUTION: how do you solve g(x)= x^2+x+12 using the quadratic formula?

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Question 283912: how do you solve g(x)= x^2+x+12 using the quadratic formula?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29=+x%5E2%2Bx%2B12 Start with the given equation.


0=+x%5E2%2Bx%2B12 Plug in g%28x%29=0


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%2Bx%2B12=0 ( notice a=1, b=1, and c=12)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=12




x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A12+%29%29%2F%282%2A1%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A1%29 Multiply -4%2A12%2A1 to get -48




x+=+%28-1+%2B-+sqrt%28+-47+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=-1%2F2%2Bsqrt%2847%29%2F2%2Ai or x=-1%2F2-sqrt%2847%29%2F2%2Ai






Note: if you've never seen or heard of complex/imaginary numbers, then the answer is simply "no solutions".