SOLUTION: I am trying to solve by using quadratic formula x^2-9x-4=6 I am confused on what to do with =6, do I rule it out when I begin simplifying? Please help

Question 88233This question is from textbook algebra
: I am trying to solve by using quadratic formula
x^2-9x-4=6
I am confused on what to do with =6, do I rule it out when I begin simplifying?
Please help This question is from textbook algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Subtract 6 from both sides

Now let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general form of the quadratic equation is:

So lets solve (notice , , and )

Plug in a=1, b=-9, and c=-10

Negate -9 to get 9

Square -9 to get 81

Multiply to get

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

Simplify the square root

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

Notice when we graph we get:

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