SOLUTION: I'm confused with this function problem. It states: For the function f(x) = x^2-2x+1 solve f(x) = 0. I'm confused about this question, please help me. Thank you.

Algebra ->  Functions -> SOLUTION: I'm confused with this function problem. It states: For the function f(x) = x^2-2x+1 solve f(x) = 0. I'm confused about this question, please help me. Thank you.      Log On


   

Question 150813: I'm confused with this function problem.
It states: For the function f(x) = x^2-2x+1 solve f(x) = 0.
I'm confused about this question, please help me. Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2-2x%2B1+ Start with the given function


0=+x%5E2-2x%2B1+ Plug in f%28x%29=0


Here are two ways to solve for x:


Method # 1 Factoring:


x%5E2-2x%2B1=0 Start with the given equation


%28x-1%29%28x-1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-1=0 or x-1=0

x=1 or x=1 Now solve for x in each case


Since we have a repeating answer, our only answer is x=1


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Method # 2 Quadratic Formula:


x%5E2-2x%2B1=0 Start with the given equation.


From x%5E2-2x%2B1, we can see that a=1, b=-2, and c=1


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-2, and c=1


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


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


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


x+=+%282+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 4 from 4 to get 0


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


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


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


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


x+=+1 or x+=+1 Simplify.


So the solution is x+=+1

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Answer:


Using either method, we get the solution x+=+1