SOLUTION: x^2-6x+9=0

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Question 542149: x^2-6x+9=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x%2B9=0 Start with the given equation.


Notice that the quadratic x%5E2-6x%2B9 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-6, and C=9


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-6, and C=9


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%289%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-36+%29%29%2F%282%281%29%29 Multiply 4%281%29%289%29 to get 36


x+=+%286+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 36 from 36 to get 0


x+=+%286+%2B-+sqrt%28+0+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+0%29%2F%282%29 Take the square root of 0 to get 0.


x+=+%286+%2B+0%29%2F%282%29 or x+=+%286+-+0%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%286%29%2F%282%29 Combine like terms.


x+=+3 or x+=+3 Simplify.


So the only solution is x+=+3


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