SOLUTION: Solve by using the quadratic formula: Z squared + 4z + 1 = 0

Question 114676: Solve by using the quadratic formula:
Z squared + 4z + 1 = 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 z:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=4, and c=1

Square 4 to get 16

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

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph (just replace z with x), we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer

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