SOLUTION: x^2+2x+9 I have tried x={-2ħsqrt(2^2-4*1*9)}/2*1 (quadratic formula: x={-bħsqrt( b^2-4ac)}/2(a)) Process: x={-2ħsqrt(2^2-4*1*9)}/2(1) x={-2ħsqrt(4-36)}/2 x=(-2/2)ħ{sqrt-3

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Question 251829: x^2+2x+9
I have tried x={-2ħsqrt(2^2-4*1*9)}/2*1
(quadratic formula: x={-bħsqrt( b^2-4ac)}/2(a))
Process:
x={-2ħsqrt(2^2-4*1*9)}/2(1)
x={-2ħsqrt(4-36)}/2
x=(-2/2)ħ{sqrt-32/2}
x=-1ħ(sqrt-32/2)
Looking for -1ħ2i*sqrt(2), but I can't get there.
I need the process to find this imaginary root.
what am I doing wrong?

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
The trick here lies in simplifying

Start with the given expression


Factor out a negative 1


Break up the square roots using the identity


Replace with (remember )


Now lets simplify :


The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 32


Factors:
1, 2, 4, 8, 16, 32


Notice how 16 is the largest perfect square, so lets factor 32 into 16*2


Factor 32 into 16*2



Break up the square roots using the identity



Take the square root of the perfect square 16 to get 4



This means that the expression simplifies to


So the expression simplifies to (just reintroduce back in)


In other words,


----------------------------------------------------------------------

Going back to , this expression simplifies to . From there, it reduces to


So the solutions are or

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