SOLUTION: Solve by using the quadratic formula: 9z squared + 12z + 4 = 0

Question 114678: Solve by using the quadratic formula:
9z squared + 12z + 4 = 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=9, b=12, and c=4

Square 12 to get 144

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 9 to get 18

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 only solution is:

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

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

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