SOLUTION: x^2-9x + 18 = 0

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Question 98883:
x^2-9x + 18 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B9%2Ax%2B18=0 ( notice a=1, b=9, and c=18)

x+=+%28-9+%2B-+sqrt%28+%289%29%5E2-4%2A1%2A18+%29%29%2F%282%2A1%29 Plug in a=1, b=9, and c=18



x+=+%28-9+%2B-+sqrt%28+81-4%2A1%2A18+%29%29%2F%282%2A1%29 Square 9 to get 81



x+=+%28-9+%2B-+sqrt%28+81%2B-72+%29%29%2F%282%2A1%29 Multiply -4%2A18%2A1 to get -72



x+=+%28-9+%2B-+sqrt%28+9+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-9+%2B-+3%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-9+%2B-+3%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-9+%2B+3%29%2F2 or x+=+%28-9+-+3%29%2F2

Lets look at the first part:

x=%28-9+%2B+3%29%2F2

x=-6%2F2 Add the terms in the numerator
x=-3 Divide

So one answer is
x=-3



Now lets look at the second part:

x=%28-9+-+3%29%2F2

x=-12%2F2 Subtract the terms in the numerator
x=-6 Divide

So another answer is
x=-6

So our solutions are:
x=-3 or x=-6

Notice when we graph x%5E2%2B9%2Ax%2B18, we get:

+graph%28+500%2C+500%2C+-16%2C+7%2C+-16%2C+7%2C1%2Ax%5E2%2B9%2Ax%2B18%29+

and we can see that the roots are x=-3 and x=-6. This verifies our answer