SOLUTION: Hi. Can I have some help finishing this expression? Find all solutions of the equation and express them in the form a + bi. x^2 + 7x + 12 = 0

Question 120811: Hi. Can I have some help finishing this expression?
Find all solutions of the equation and express them in the form a + bi.
x^2 + 7x + 12 = 0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=7, and c=12

Square 7 to get 49

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

which look like this in form

or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

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