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

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Question 93653: Solve the equation algebraically.
2x-x^2-18x+9=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x-x%5E2-18x%2B9=0

-x%5E2-16x%2B9=0 Combine like terms

Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve -x%5E2-16%2Ax%2B9=0 ( notice a=-1, b=-16, and c=9)

x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A-1%2A9+%29%29%2F%282%2A-1%29 Plug in a=-1, b=-16, and c=9



x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A-1%2A9+%29%29%2F%282%2A-1%29 Negate -16 to get 16



x+=+%2816+%2B-+sqrt%28+256-4%2A-1%2A9+%29%29%2F%282%2A-1%29 Square -16 to get 256 (note: remember when you square -16, you must square the negative as well. This is because %28-16%29%5E2=-16%2A-16=256.)



x+=+%2816+%2B-+sqrt%28+256%2B36+%29%29%2F%282%2A-1%29 Multiply -4%2A9%2A-1 to get 36



x+=+%2816+%2B-+sqrt%28+292+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)



x+=+%2816+%2B-+2%2Asqrt%2873%29%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%2816+%2B-+2%2Asqrt%2873%29%29%2F-2 Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

x+=+%2816+%2B+2%2Asqrt%2873%29%29%2F-2 or x+=+%2816+-+2%2Asqrt%2873%29%29%2F-2


Now break up the fraction


x=%2B16%2F-2%2B2%2Asqrt%2873%29%2F-2 or x=%2B16%2F-2-2%2Asqrt%2873%29%2F-2


Simplify


x=-8-sqrt%2873%29 or x=-8%2Bsqrt%2873%29


So these expressions approximate to

x=-16.5440037453175 or x=0.54400374531753


So our solutions are:
x=-16.5440037453175 or x=0.54400374531753

Notice when we graph -x%5E2-16%2Ax%2B9, we get:



when we use the root finder feature on a calculator, we find that x=-16.5440037453175 and x=0.54400374531753.So this verifies our answer