SOLUTION: Solve the equation algebraically. 2x-x^2-18x+9=0

Question 93653: Solve the equation algebraically.
2x-x^2-18x+9=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Combine like terms

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=-16, and c=9

Negate -16 to get 16

Square -16 to get 256 (note: remember when you square -16, you must square the negative as well. This is because .)

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 , 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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